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

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

[3] Optimal Sobolev norms and the Lp Minkowski problem

[4] Calabi-Yau manifolds with isolated conical singularities

[5] Semiclassical measures on hyperbolic surfaces have full support

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

[7] Wave propagation speed on fractals

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

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

[10] Uncertain Multilevel Programming: Algorithm and Applications

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

[12] On improved fractional Sobolev–Poincaré inequalities

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

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

[15] Multiplication in Sobolev spaces, revisited

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

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

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

[19] Evolution of the two dimensional Boussinesq system

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

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

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

[23] A geometric approach to generalized Stokes conjectures

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

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

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

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

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

[29] 2D Homogeneous Solutions to the Euler Equation

[30] The logarithmic Minkowski problem

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

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

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

[34] Spectroscopic imaging of a dilute cell suspension

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

[36] Monge–Ampère equations in big cohomology classes

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

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

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

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

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

[42] Partial differential equations in several complex variables

[43] Uniform bound and convergence for elliptic homogenization problems

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

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

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

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

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

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

[50] Random conformal weldings

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

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

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

[54] Elliptic and parabolic equations in fractured media

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

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

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

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

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

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

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

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

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

[64] Curvature estimates for immersed hypersurfaces in Riemannian manifolds

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

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

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

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

[69] Spectral analysis of the subelliptic oblique derivative problem

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

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

[72] Nonhexagonal lattices from a two species interacting system

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

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

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

[76] A Nonlocal Stokes system with volume constraints

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

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

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

[80] Convergence for elliptic equations in periodic perforated domains

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

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

[83] Yamabe type equations on graphs

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

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

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

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

[88] Kazdan–Warner equation on graph

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

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

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

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

[93] On a new class of partial differential equations

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

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

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

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

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

[99] Directional Poincaré inequalities along mixing flows

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

[101] On the formation of trapped surfaces

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[122] Flow on sweeping networks

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

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

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

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

[127] Hölder regularity for degenerate parabolic obstacle problems

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

[129] A four-dimensional Neumann ovaloid

[130] Quermassintegral preserving curvature flow in hyperbolic space

[131] Maximal Marcinkiewicz multipliers

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

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

[134] Homogenization and boundary layers

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

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

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

[138] Effective fronts of polygon shapes in two dimensions

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

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

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

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

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

[144] Effective Fronts of Polytope Shapes

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

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

[147] Invertibility of nonsmooth mappings

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

[149] Energy method for Boltzmann equation

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

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

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

[153] Uniform exponential stability of the Ekman spiral

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[168] Calculus of variations on locally finite graphs

[169] Harnack and mean value inequalities on graphs

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

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

[172] Some remarks on boundary operators of Bessel extensions

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

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

[175] Polynomial hulls and proper analytic disks

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

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

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

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

[180] Well-posedness for Hall-magnetohydrodynamics

[181] Thin film epitaxy with or without slope selection

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

[183] Front propagation in heterogeneous media

[184] On Singularity Formation of a Nonlinear Nonlocal System

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

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

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

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

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

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

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

[192] On the Carleson duality

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

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

[195] Numerical methods for oscillatory solutions to hyperbolic problems

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

[197] On Singularity Formation of a 3D Model for Incompressible Navier-Stokes Equations

[198] Compressible Euler equations with vacuum

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

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

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

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

[203] The dual Orlicz-Minkowski problem

[204] Existence of local solutions for the Boltzmann equation without angular cutoff

[205] Asymptotic analysis for time harmonic wave problems with small wave number

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

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

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

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

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

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

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

[213] Self-similar spreading in a merging-splitting model of animal group size

[214] Global solution for the 3D gravity water waves system above a flat bottom

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

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

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

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

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

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

[221] Regularity for a fractional p-Laplace equation

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

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

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

[225] Cutoff Boltzmann equation with polynomial perturbation near Maxwellian

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

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

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

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

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

[231] Inverse curvature flow in anti-de Sitter-Schwarzschild manifold

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

[233] Global stability for solutions to the exponential PDE describing epitaxial growth

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

[235] 1-minimization method for link flow correction

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

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

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

[239] A coupled chemotaxis-fluid model: Global existence

[240] Relaxation and diffusion enhanced dispersive waves

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

[242] Macroscopic fluid modes with localized kinetic upscaling effects

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

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

[245] On incompressible Navier-Stokes dynamics: a new approach for analysis and computation

[246] Evolutions of the momentum density, deformation tensor and the nonlocal term of the Camassa-Holm equation

[247] A domain decomposition method for semilinear hyperbolic systems with two-scale relaxations

[248] Eptaxial growth without slope selection: energetics, coarsening, and dynamic scaling

[249] Global existence for a thin film equation with subcritical mass

[250] Regularizing effect and local existence for the non-cutoff Boltzmann equation

[251] Zeros of the deformed exponential function

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

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

[254] Partial regularity for weak solutions to a PDE system with cubic nonlinearities

[255] A vicinal surface model for epitaxial growth with logarithmic free energy

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