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

[2] Optimal Sobolev norms and the Lp Minkowski problem

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

[4] Calabi-Yau manifolds with isolated conical singularities

[5] Semiclassical measures on hyperbolic surfaces have full support

[6] Wave propagation speed on fractals

[7] Uncertain Multilevel Programming: Algorithm and Applications

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

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

[10] On improved fractional Sobolev–Poincaré inequalities

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

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

[13] Evolution of the two dimensional Boussinesq system

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

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

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

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

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

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

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

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

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

[24] 2D Homogeneous Solutions to the Euler Equation

[25] The logarithmic Minkowski problem

[26] Spectroscopic imaging of a dilute cell suspension

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

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

[29] Uniform bound and convergence for elliptic homogenization problems

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

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

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

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

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

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

[36] Elliptic and parabolic equations in fractured media

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

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

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

[40] A geometric approach to generalized Stokes conjectures

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

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

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

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

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

[46] Random conformal weldings

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[61] Convergence for elliptic equations in periodic perforated domains

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

[63] Spectral analysis of the subelliptic oblique derivative problem

[64] Nonhexagonal lattices from a two species interacting system

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

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

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

[68] Curvature estimates for immersed hypersurfaces in Riemannian manifolds

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

[70] On a new class of partial differential equations

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

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

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

[74] Partial differential equations in several complex variables

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

[76] A Nonlocal Stokes system with volume constraints

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

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

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

[80] Monge–Ampère equations in big cohomology classes

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

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

[83] Yamabe type equations on graphs

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

[85] Multiplication in Sobolev spaces, revisited

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

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

[88] Kazdan–Warner equation on graph

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

[106] Flow on sweeping networks

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

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

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

[110] Hölder regularity for degenerate parabolic obstacle problems

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

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

[113] On the formation of trapped surfaces

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

[115] Directional Poincaré inequalities along mixing flows

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

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

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

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

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

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

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

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

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

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

[126] Homogenization and boundary layers

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

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

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

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

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

[132] A four-dimensional Neumann ovaloid

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

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

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

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

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

[138] Quermassintegral preserving curvature flow in hyperbolic space

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

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

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

[142] Invertibility of nonsmooth mappings

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

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

[145] Uniform exponential stability of the Ekman spiral

[146] Some remarks on boundary operators of Bessel extensions

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

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

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

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

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

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

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

[154] Energy method for Boltzmann equation

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

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

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

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

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

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

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

[162] On Singularity Formation of a Nonlinear Nonlocal System

[163] Well-posedness for Hall-magnetohydrodynamics

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

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

[166] Polynomial hulls and proper analytic disks

[167] Maximal Marcinkiewicz multipliers

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

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

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

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

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

[173] Numerical methods for oscillatory solutions to hyperbolic problems

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

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

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

[177] On the Carleson duality

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

[179] The dual Orlicz-Minkowski problem

[180] Thin film epitaxy with or without slope selection

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

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

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

[184] Regularity for a fractional p-Laplace equation

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

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

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

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

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

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

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

[192] Compressible Euler equations with vacuum

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

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

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

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

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

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

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

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

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

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

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

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

[205] Relaxation and diffusion enhanced dispersive waves

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

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

[208] 1-minimization method for link flow correction

[209] Macroscopic fluid modes with localized kinetic upscaling effects

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

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

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

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

[214] Front propagation in heterogeneous media

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

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

[217] Convergence of point vortex method for 2-D vortex sheet

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

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

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

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

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

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

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

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

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

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

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

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

[230] P-Euler equations and p-Navier-Stokes equations,

[231] On the Expanding Configurations of Viscous Radiation Gaseous Stars: Isentropic and Thermodynamic Models

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

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

[234] Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow

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

[236] A model of radiational gaseous stars

[237] Time periodic solution to the compressible Navier-Stokes equations in a periodic domain

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

[239] Cauchy problems for Keller–Segel type time–space fractional diffusion equation

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

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

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

[243] Well-posedness of thermal layer equations for inviscid compressible flows

[244] Gradient estimates for parabolic and elliptic systems from linear laminates

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

[246] Kinetic and viscous boundary layers for the Broadwell equations

[247] Global solutions to the Boltzmann equation with external forces

[248] Weak solutions of general systems of hyperbolic conservation laws

[249] Estimates on the Stokes pressure by partitioning the energy of harmonic functions

[250] Maximal monotone operator theory and its applications to thin film equation in epitaxial growth on vicinal surface

[251] Zeros of the deformed exponential function

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

[253] Large oscillations arising from a dispersive numerical scheme

[254] On $l_p$-estimates for elliptic and parabolic equations with $a_p$ weights

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

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

[257] Monge-Ampere equation with bounded periodic data

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

[259] Almost Global Solutions to t