[1] A model of radiational gaseous stars

[2] Quermassintegral preserving curvature flow in hyperbolic space

[3] Existence of Multi-dimensional Contact Discontinuities for the Ideal Compressible Magnetohydrodynamics

[4] Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems

[5] Multiplication in Sobolev spaces, revisited

[6] Global classical and weak solutions to the three-dimensional full compressible Navier-Stokes system with vacuum and large oscillations

[7] Trace theorems for some nonlocal energy spaces with heterogeneous localization

[8] Wave propagation speed on fractals

[9] Calabi-Yau manifolds with isolated conical singularities

[10] L2-contraction of large planar shock waves for multi-dimensional scalar viscous conservation laws

[11] Semiclassical measures on hyperbolic surfaces have full support

[12] Efficient Parallel Simulation of Blood Flows in Abdominal Aorta

[13] Optimal Sobolev norms and the Lp Minkowski problem

[14] On improved fractional Sobolev–Poincaré inequalities

[15] A geometric approach to generalized Stokes conjectures

[16] Spectral analysis and computation of effective diffusivities in space-time periodic incompressible flows

[17] Generalized characteristics and Lax-Oleinik operators: global theory

[18] Partial differential equations in several complex variables

[19] Contact discontinuity with general perturbations for gas motions

[20] Uncertain Multilevel Programming: Algorithm and Applications

[21] Estimates of the gaps between consecutive eigenvalues of Laplacian

[22] Global existence of smooth solutions and convergence to Barenblatt solutions for the physical vacuum free boundary problem of compressible Euler equations with damping

[23] On the Free Surface Motion of Highly Subsonic Heat-conducting Inviscid Flows

[24] Monge–Ampère equations in big cohomology classes

[25] Existence and nonexistence of traveling waves and reaction-diffusion front propagation in periodic media

[26] On classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations with vacuum

[27] On the formation of shocks for quasilinear wave equations

[28] A Holder estimate for non-uniform elliptic equations in a random medium

[29] Weyl-type asymptotic formula for Schr\"odinger operators on unbounded fractal spaces

[30] The explicit formulae for scaling limits in the ergodic decomposition of infinite Pickrell measures

[31] Passive Array Correlation-Based Imaging in a Random Waveguide

[32] Global regularity for the 3D finite depth capillary water waves

[33] Instantaneous unboundedness of the entropy and uniform positivity of the temperature for the compressible Navier-Stokes equations with fast decay density

[34] The existence of the solution of the wave equation on graphs

[35] Existence and blowup behavior of global strong solutions to the two-dimensional barotropic compressible Navier–Stokes system with vacuum and large initial data

[36] Cutoff Boltzmann equation with polynomial perturbation near Maxwellian

[37] Stability of contact discontinuity for the Boltzmann equation

[38] Blow up for the critical generalized Korteweg–de Vries equation. I: Dynamics near the soliton

[39] Refined hyper-contractivity and uniqueness for the Keller-Segel equations

[40] On a doubly critical Schrodinger system in R4 with steep potential wells

[41] Global solutions of the gravity-capillary water-wave system in three dimensions

[42] Weak solution of a continuum model for vicinal surface in the attachment-detachment-limited regime

[43] Front Quenching in G-equation Model Induced by Straining of Cellular Flow

[44] Mean Field Equation of Liouville Type with Singular Data Topological Degree

[45] A simple proof of the Cucker-Smale flocking dynamics and mean-field limit

[46] Harnack and mean value inequalities on graphs

[47] On convolution groups of completely monotone sequences/functions and fractional calculus

[48] Mean field equations, hyperelliptic curves and modular forms: I

[49] Large time average of reachable sets and Applications to Homogenization of interfaces moving with oscillatory spatio-temporal velocity

[50] The logarithmic Minkowski problem

[51] On the regularity of solutions to a generalization of the Minkowski problem

[52] Effective fronts of polygon shapes in two dimensions

[53] Effective Fronts of Polytope Shapes

[54] Calculus of variations on locally finite graphs

[55] Basic themes and pretty problems of nonlinear solid mechanics

[56] On the constant scalar curvature K\"ahler metrics-apriori estimates

[57] Heterogeneously localized nonlocal operators, boundary traces and variational problems

[58] Stable hypersurfaces with zero scalar curvature in Euclidean space

[59] Asymptotic behavior of equilibrium states of reaction–diffusion systems with mass conservation

[60] Uniqueness of topological solutions and the structure of solutions for the Chern-Simons system with two Higgs particles

[61] A heat flow for the mean field equation on a finite graph

[62] Higher integrability for vector-valued parabolic quasi-minimizers on metric measure spaces

[63] 2D Homogeneous Solutions to the Euler Equation

[64] Some compactness criteria for weak solutions of time fractional PDEs

[65] Generalization of Selberg’s $$ \frac{3}{{16}} $$ theorem and affine sieve

[66] Corrector theory for elliptic equations with long-range correlated random potential

[67] Stability of wave patterns to the inflow problem of full compressible NavierStokes equations

[68] L^p gradient estimate for elliptic equations with high-contrast conductivities in R^n

[69] Minimizers of Caffarelli-Kohn-Nirenberg inequalities with the singularity on the boundary.

[70] Dynamic and steady states for multi-dimensional Keller-Segel model with diffusion exponent m > 0

[71] The existence and nonexistence of global solutions for a semilinear heat equation on graphs

[72] Transonic Shocks for the Full Compressible Euler Systems in a general two-dimensional de Laval nozzle

[73] Energy method for Boltzmann equation

[74] Entire solutions with merging three fronts to the Allen-Cahn equation

[75] Random conformal weldings

[76] Regularity of the Schrödinger equation for the harmonic oscillator

[77] Curvature estimates for immersed hypersurfaces in Riemannian manifolds

[78] Corrector Analysis of a Heterogeneous Multi-scale Scheme for Elliptic Equations with Random Potential

[79] On the Finite-time Blowup of a 1D Model for the 3D Axisymmetric Euler Equations

[80] Global well-posedness of the three-dimensional primitive equations with only horizontal viscosity and diffusion

[81] On a K-component elliptic system with the Sobolev critical exponent in high dimensions: the repulsive case

[82] Existence and decay estimates for time dependent parabolic equation with application to DuncanMortensenZakai equation

[83] Well-posedness for the motion of physical vacuum of the three-dimensional compressible Euler equations with or without self-gravitation

[84] Least action principles for incompressible flows and optimal transport between shapes

[85] Spectroscopic imaging of a dilute cell suspension

[86] Evolution of the two dimensional Boussinesq system

[87] Two exponential-type integrators for the “good” Boussinesq equation

[88] Hölder regularity for degenerate parabolic obstacle problems

[89] An Efficient Semi-Implicit Immersed Boundary Method for the Navier-Stokes Equations

[90] Compression bounds for Lipschitz maps from the Heisenberg group to$L$_{1}

[91] Resonance-free region in scattering by a strictly convex obstacle

[92] Exact number and non-degeneracy of critical points of multiple Green functions on rectangular tori

[93] Propagation of uniform boundedness of entropy and inhomogeneous regularities for viscous and heat conductive gases with far field vacuum in three dimensions

[94] The Fu–Yau equation with negative slope parameter

[95] On a two-component Bose-Einstein condensate with steep potential wells

[96] Global Well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional Compressible Navier-Stokes equations

[97] The p-capacitary Orlicz–Hadamard variational formula and Orlicz–Minkowski problems

[98] Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density

[99] A generalized Sz. Nagy inequality in higher dimensions and the critical thin film equation

[100] Asymptotic behavior of solutions to a class of diffusive predator-prey systems

[101] Pointwise estimate for elliptic equations in periodic perforated domains

[102] Analytical validation of a continuum model for the evolution of a crystal surface in multiple space dimensions

[103] Nonhexagonal lattices from a two species interacting system

[104] Uniform bound and convergence for elliptic homogenization problems

[105] Local-in-space estimates near initial time for weak solutions of the Navier-Stokes equations and forward self-similar solutions

[106] Self-dual radial non-topological solutions to a competitive Chern-Simons model

[107] Entropy-bounded solutions to the one-dimensional heat conductive compressible Navier--Stokes equations with far field vacuum

[108] Removable singularity of positive solutions for a critical elliptic system with isolated singularity

[109] A volume preserving flow and the isoperimetric problem in warped product spaces

[110] Homogenization of interfaces moving in spatially random temporally periodic environment

[111] Non-uniform elliptic equations in convex Lipschitz domains

[112] Starshaped compact hypersurfaces with prescribed Weingarden curvature in warped product manifolds

[113] On Weyl's embedding problem in Riemannian manifolds

[114] Directional Poincaré inequalities along mixing flows

[115] Strong ill-posedness of the incompressible Euler equation in borderline Sobolev spaces

[116] Stability of the Superposition of a Viscous Contact Wave with Two Rarefaction Waves to the Bipolar Vlasov--Poisson--Boltzmann System

[117] Long-time behavior of solutions to the bipolar hydrodynamic model of semiconductors with boundary effect

[118] A degenerate p-Laplacian Keller-Segel model

[119] Convergence for elliptic equations in periodic perforated domains

[120] Kazdan–Warner equation on graph

[121] Normalized solutions for a coupled Schr\"odinger system

[122] Global integral gradient bounds for quasilinear equations below or near the natural exponent

[123] Yamabe type equations on graphs

[124] Uniform $L^{\infty}$ boundedness for a degenerate parabolic-parabolic Keller-Segel model

[125] Mean Field Equations, Hyperelliptic curves and modular forms II

[126] Elliptic and parabolic equations in fractured media

[127] A Nonlocal Stokes system with volume constraints

[128] Global uniqueness of the minimal sphere in the Atiyah--Hitchin manifold

[129] On the topology of the set of singularities of a solution of the Hamilton-Jacobi equation

[130] Uniqueness of topological multivortex solutions in the Maxwell-Chern-Simons model

[131] Global existence of solutions to a tear film model with locally elevated evaporation rates

[132] Target Identification Using Dictionary Matching of Generalized Polarization Tensors

[133] Stability of Traveling Waves of Nonlinear Schrödinger Equation with Nonzero Condition at Infinity

[134] A strong stability condition on minimal submanifolds and its implications

[135] Stability of Contact Waves for Navier-Stokes Equations and Boltzmann Equation

[136] On the formation of trapped surfaces

[137] Spikes of the two-component elliptic system in R4 with the critical Sobolev exponent

[138] Global regularity for the Monge-Ampère equation with natural boundary condition

[139] The solution structure of the O(3) sigma model in a Maxwell-Chern-Simons theory

[140] Spectral analysis of the subelliptic oblique derivative problem

[141] The quenching rate for a nonlocal problem arising in the micro-electro mechanical system

[142] Nonlinear asymptotic stability of the Lane-Emden solutions for the viscous gaseous star problem with degenerate density dependent viscosities

[143] Fluctuations in the Homogenization of Semilinear Equations with Random Potentials

[144] Asymptotic behavior of positive singular solutions to fractional Hardy-Henon equations

[145] Modeling light bullets with the two-dimensional sineGordon equation

[146] A proof of Bondesson’s conjecture on stable densities

[147] Entropy bounded solutions to the one-dimensional compressible Navier-Stokes equations with zero heat conduction and far field vacuum

[148] Spectral asymptotics of one-dimensional graph-directed self-similar measures with overlaps

[149] Serrin-type blowup criterion for viscous, compressible, and heat conducting Navier-Stokes and magnetohydrodynamic flows

[150] Classification of nondegeneracy of Toda system with singular sources

[151] $R$ -Boundedness versus $\gamma$ -boundedness

[152] Holder estimate for non-uniform parabolic equations in highly heterogeneous media

[153] Well-posedness for the Keller-Segel equation with fractional Laplacian and the theory of propagation of chaos

[154] Instability of spherical naked singularities of a scalar field under gravitational perturbations

[155] Embedded minimal tori in$S$^{3}and the Lawson conjecture

[156] On a new class of partial differential equations

[157] Local well-posedness of isentropic compressible Navier-Stokes equations with vacuum

[158] Accurate Solution and Gradient Computation for Elliptic Interface Problems with Variable Coefficients

[159] Operator-Lipschitz functions in Schatten–von Neumann classes

[160] Front propagation in heterogeneous media

[161] Extrapolation from $A_{\infty}^{\rho,\infty}$ , vector-valued inequalities and applications in the Schrödinger settings

[162] On the constant scalar curvature K\"ahler metrics-general automorphism group

[163] Heat equations defined by a class of fractal measures

[164] Global well-posedness of the one-dimensional compressible navier-stokes equations with constant heat conductivity and nonnegative density

[165] A four-dimensional Neumann ovaloid

[166] On the role of Riesz potentials in Poisson's equation and Sobolev embeddings

[167] On the quenching behavior of the MEMS with fringing field

[168] The convergence Newton polygon of a$p$-adic differential equation II: Continuity and finiteness on Berkovich curves

[169] Polynomial hulls and proper analytic disks

[170] Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model

[171] Convergence of vortex methods for weak solutions to the 2-D Euler equations with vortex sheets data

[172] Zeros of the deformed exponential function

[173] Perturbation theorems for Hele-Shaw flows and their applications

[174] Topological multivortex solutions for the Chern-Simons system with two Higgs particles

[175] Flow on sweeping networks

[176] Continuum dynamics of the intention field under weakly cohesive social interaction

[177] Uniqueness of positive solution to some coupled cooperative variational elliptic systems

[178] Nonlinear stability of discrete shocks for systems of conservation laws

[179] On a Class of Functional Inequalities and their Applications to Fourth-Order Nonlinear Parabolic Equations

[180] Addendum: 2D homogeneous solutions to the Euler equation

[181] H\"{o}lder Continuous Solutions to the Three-dimensional Prandtl System

[182] An accurate front capturing scheme for tumor growth models with a free boundary limit

[183] Maximal Marcinkiewicz multipliers

[184] Compressible NavierStokes equations with degenerate viscosity coefficient and vacuum

[185] Regularity for a fractional $p$-Laplace equation

[186] The dual Orlicz-Minkowski problem

[187] Existence and uniqueness of solutions for Duncan-Mortensen-Zakai equations

[188] Invertibility of nonsmooth mappings

[189] An improved Combes–Thomas estimate of magnetic Schrödinger operators

[190] Stochastic homogenization of viscous superquadratic Hamilton–Jacobi equations in dynamic random environment

[191] A sharp lower bound for the log canonical threshold

[192] Phase transitions, hysteresis, and hyperbolicity for self-organized alignment dynamics

[193] Homogenization and boundary layers

[194] Uniform exponential stability of the Ekman spiral

[195] Maximization of the second non-trivial Neumann eigenvalue

[196] Well-posedness for Hall-magnetohydrodynamics

[197] General volumes in the Orlicz-Brunn-Minkowski theory and a related Minkowski Problem I

[198] Nonlinear Differential Equations in Geometry and Physics.

[199] The weyl problem in warped product spaces

[200] A random particle blob method for the Keller-Segel equation and convergence analysis

[201] Stability and convergence of efficient Navier-Stokes solvers via a commutator estimate

[202] Curvature effect in shear flow: slowdown of turbulent flame speeds with Markstein number

[203] Local Well-posedness of Strong Solutions to the Three-dimensional Compressible Primitive Equations

[204] Nonlinear stability of rarefaction waves for the Boltzmann equation

[205] Two nonlinear compactness theorems in L p (0,T;B) L p ( 0 , T ; B ) mathContainer Loading Mathjax

[206] Continuum Limit of a Mesoscopic Model with Elasticity of Step Motion on Vicinal Surfaces

[207] Thin film epitaxy with or without slope selection

[208] On the incompressible fluid limit and the vortex motion law of the nonlinear Schrdinger equation

[209] Well-posedness and singular limit of a semilinear hyperbolic relaxation system with a two-scale discontinuous relaxation rate

[210] Compressible Euler equations with vacuum

[211] Boundary integral operators and boundary value problems for Laplace’s equation

[212] Global stability of wave patterns for compressible Navier-Stokes system with free boundary

[213] Quasiconformality, homeomorphisms between metric measure spaces preserving quasiminimizers, and uniform density property

[214] A new type of non-topological bubbling solutions to a competitive Chern-Simons model

[215] MHD boundary layers in Sobolev spaces without monotonicity, II: Convergence theory

[216] Global infinite energy solutions for the 2D gravity water waves system

[217] Existence of multidimensional traveling waves in the transport of reactive solutes through periodic porous media

[218] The primitive equations approximation of the anisotropic horizontally viscous Navier-Stokes equations

[219] Large-scale dynamics of Mean-Field Games driven by local Nash equilibria

[220] An asymptotic propertiy of the Camassa-Holm equation

[221] On a Schrodinger-Landau-Lifshitz system: Variational structure and numerical methods

[222] Ultra-contractivity for Keller-Segel model with diffusion exponent m>1-2/d

[223] Comparisons between sine-Gordon and perturbed nonlinear Schrdinger equations for modeling light bullets beyond critical collapse

[224] A note on $L^{\infty}$-bound and uniqueness to a degenerate Keller-Segel model

[225] Non-uniqueness of Weak Solutions to Hyperviscous Navier-Stokes Equations - On Sharpness of J.-L. Lions Exponent

[226] Convergence analysis of the vortex blob method for the b-equation

[227] Boundary layer behavior in the fluid-dynamic limit for a nonlinear model Boltzmann equation

[228] Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows

[229] A reverse quasiconformal composition problem for Qα(Rn)

[230] Numerical methods for oscillatory solutions to hyperbolic problems

[231] Existence and nonexistence to exterior Dirichlet problem for Monge-Ampere equation

[232] Evaluating solutions on an elliptic problem in a gravitational gauge field theory

[233] Limiting distribution of elliptic homogenization error with periodic diffusion and random potential

[234] Hydrodynamic limit of the Boltzmann equation with contact discontinuities

[235] A normality criterion involving rotations and dilations in the argument

[236] Error estimate of a random particle blob method for the Keller-Segel equation

[237] Global existence of classical solutions to the Vlasov-Poisson-Boltzmann system

[238] Global small solutions of heat conductive compressible Navier-Stokes equations with vacuum: smallness on scaling invariant quantity

[239] A note on Monge–Amp`ere Keller–Segel equation

[240] Analysis of polymeric flow models and related compactness theorems in weighted spaces

[241] Non-uniqueness of Admissible Weak Solutions to Compressible Euler Systems with Source Terms

[242] Qualitative analysis for an elliptic system in the punctured space

[243] Existence of solutions to the even dual minkowski problem

[244] MHD Boundary Layers Theory in Sobolev Spaces Without Monotonicity I: Well-Posedness Theory

[245] Dynamics in a kinetic model of oriented particles with phase transition

[246] A global unique solvability of entropic weak solution to the one-dimensional pressureless Euler system with a flocking dissipation

[247] Asymptotic spreading of KPP reactive fronts in incompressible space-time random flows

[248] Blow-up, zero $\alpha$ limit and the Liouville type theorem for the Euler-Poincar\'{e} equations

[249] Global large time self-similarity of a thermal-diffusive combustion system with critical nonlinearity

[250] Linear elliptic equations in composite media with anisotropic fibres

[251] Well-posedness in Gevrey function space for the three-dimensional Prandtl equations

[252] On the solutions to a Liouville-type system involving singularity

[253] Global weak entropy solution to Doi-Saintillan-Shelley model for active and passive rod-like and ellipsoidal particle suspensions

[254] Existence of global smooth solutions for Euler equations with symmetry (II)

[255] Fu-Yau Hessian equation