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

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

[3] Multiplication in Sobolev spaces, revisited

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

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

[6] Calabi-Yau manifolds with isolated conical singularities

[7] Wave propagation speed on fractals

[8] Optimal Sobolev norms and the Lp Minkowski problem

[9] Semiclassical measures on hyperbolic surfaces have full support

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

[11] On improved fractional Sobolev–Poincaré inequalities

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

[13] A geometric approach to generalized Stokes conjectures

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

[15] A model of radiational gaseous stars

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

[17] Uncertain Multilevel Programming: Algorithm and Applications

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

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

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

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

[22] Partial differential equations in several complex variables

[23] Contact discontinuity with general perturbations for gas motions

[24] Monge–Ampère equations in big cohomology classes

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

[26] Quermassintegral preserving curvature flow in hyperbolic space

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

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

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

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

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

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

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

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

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

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

[37] Harnack and mean value inequalities on graphs

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

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

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

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

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

[43] Effective fronts of polygon shapes in two dimensions

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

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

[46] Effective Fronts of Polytope Shapes

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

[48] Stability of contact discontinuity for the Boltzmann equation

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

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

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

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

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

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

[55] Cutoff Boltzmann equation with polynomial perturbation near Maxwellian

[56] Evolution of the two dimensional Boussinesq system

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

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

[59] 2D Homogeneous Solutions to the Euler Equation

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

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

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

[63] The logarithmic Minkowski problem

[64] Calculus of variations on locally finite graphs

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

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

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

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

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

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

[71] Spectroscopic imaging of a dilute cell suspension

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

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

[74] Random conformal weldings

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

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

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

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

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

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

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

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

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

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

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

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

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

[88] Uniform bound and convergence for elliptic homogenization problems

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

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

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

[92] Curvature estimates for immersed hypersurfaces in Riemannian manifolds

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

[94] Hölder regularity for degenerate parabolic obstacle problems

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[111] Nonhexagonal lattices from a two species interacting system

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

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

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

[115] Directional Poincaré inequalities along mixing flows

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

[117] Elliptic and parabolic equations in fractured media

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

[119] Kazdan–Warner equation on graph

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

[121] Energy method for Boltzmann equation

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

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

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

[125] On the formation of trapped surfaces

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

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

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

[129] Yamabe type equations on graphs

[130] Spectral analysis of the subelliptic oblique derivative problem

[131] A Nonlocal Stokes system with volume constraints

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

[133] On a new class of partial differential equations

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[149] Flow on sweeping networks

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

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

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

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

[154] Convergence for elliptic equations in periodic perforated domains

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

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

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

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

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

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

[161] Front propagation in heterogeneous media

[162] A four-dimensional Neumann ovaloid

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

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

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

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

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

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

[169] Polynomial hulls and proper analytic disks

[170] Zeros of the deformed exponential function

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

[172] Invertibility of nonsmooth mappings

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

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

[175] Maximal Marcinkiewicz multipliers

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

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

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

[179] Homogenization and boundary layers

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

[181] The dual Orlicz-Minkowski problem

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

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

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

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

[186] Thin film epitaxy with or without slope selection

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

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

[189] Uniform exponential stability of the Ekman spiral

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

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

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

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

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

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

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

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

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

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

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

[201] Nonlinear Differential Equations in Geometry and Physics.

[202] Well-posedness for Hall-magnetohydrodynamics

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[221] Spectral theory for the Weil–Petersson Laplacian on the Riemann moduli space

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

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

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

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

[226] Compressible Euler equations with vacuum

[227] The weyl problem in warped product spaces

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

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

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

[231] Numerical methods for oscillatory solutions to hyperbolic problems

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

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

[234] On Singularity Formation of a Nonlinear Nonlocal System

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

[236] On the Carleson duality

[237] Ground-state solutions of a two-component elliptic system in R4 with the Sobolev critical exponent

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

[239] Existence and uniqueness of global weak solution to a kinetic model for the sedimentation of rod-like particles

[240] Some remarks on boundary operators of Bessel extensions

[241] Hydrodynamic models of self-organized dynamics: derivation and existence theory

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

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

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

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

[246] Time regularity of the solutions to second order hyperbolic equations

[247] Multidimensional Degenerate Keller–Segel System with Critical Diffusion Exponent $2n/(n+2)$ Read More: http://epubs.siam.org/doi/abs/10.1137/110839102

[248] Structural stability and bifurcation for 2D incompressible flows with symmetry

[249] An exact solution for Stokes flow in a channel with arbitrarily large wall permeability

[250] 1-minimization method for link flow correction

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

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

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

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