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Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 12/2011, Volume 18, Issue 6, pp. 707 - 735
In this paper we consider the following 2D Boussinesq–Navier–Stokes systems $${\begin{array}{lll}\partial_t u + u \cdot \nabla u + \nabla p = - \nu |D|^\alpha... 
Para-differential calculus | Regularization effect | Global well-posedness | Analysis | 35Q35 | 35B33 | 76D03 | Boussinesq system | Mathematics | 76D05 | MATHEMATICS, APPLIED | MAXIMUM PRINCIPLE | Mathematics - Analysis of PDEs
Journal Article
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 01/2015, Volume 68, Issue 1, pp. 61 - 111
An important problem in gas and fluid dynamics is to understand the behavior of vacuum states, namely the behavior of the system in the presence of a vacuum.... 
MATHEMATICS | WATER-WAVES | VISCOSITY METHOD | MATHEMATICS, APPLIED | NAVIER-STOKES EQUATIONS | FLUID-DYNAMICS | HYPERBOLIC SYSTEMS | ISENTROPIC GAS-DYNAMICS | FREE-BOUNDARY | GLOBAL SMOOTH SOLUTIONS | SURFACE-TENSION | ELLIPTICAL OPERATORS
Journal Article
Journal de mathématiques pures et appliquées, ISSN 0021-7824, 2009, Volume 91, Issue 6, pp. 583 - 597
We prove that the Korteweg–de Vries initial-value problem is globally well-posed in H − 3 / 4 ( R ) and the modified Korteweg–de Vries initial-value problem is... 
Low regularity | Global well-posedness | Korteweg–de Vries equation | Korteweg-de Vries equation | MATHEMATICS | MATHEMATICS, APPLIED | REGULARITY | DISPERSIVE EQUATIONS | ILL-POSEDNESS | KDV | SCATTERING
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 09/2015, Volume 259, Issue 5, pp. 1722 - 1742
This paper is concerned with an initial–boundary value problem of the incompressible Navier–Stokes equations with density-dependent viscosity in a smooth... 
Density-dependent viscosity | Global existence | Incompressible Navier–Stokes equations | Strong solutions | Incompressible Navier-Stokes equations | EXISTENCE | FLUIDS | MATHEMATICS | BOUNDARY-VALUE PROBLEM | SOLVABILITY | FLOWS | Fluid dynamics
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2016, Volume 443, Issue 2, pp. 1142 - 1157
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 10/2018, Volume 265, Issue 8, pp. 3792 - 3840
We study the local and global solutions of the generalized derivative nonlinear Schrödinger equation i∂tu+Δu=P(u,u‾,∂xu,∂xu‾), where each monomial in P is of... 
Derivative nonlinear Schrödinger equations | Local well-posedness | Global well-posedness | EXISTENCE | MATHEMATICS | REGULARITY | SCATTERING | Derivative nonlinear Schrodinger equations
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2011, Volume 251, Issue 12, pp. 3381 - 3402
We consider the defocusing energy-critical nonlinear Schrödinger equation of fourth order i u t + Δ 2 u = − | u | 8 d − 4 u . We prove that any finite energy... 
Defocusing | Fourth order Schrödinger equations | Global well-posedness | Scattering | Energy-critical | Fourth order schrödinger equations | MATHEMATICS | Fourth order Schrodinger equations | RADIAL DATA | BLOW-UP
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2018, Volume 264, Issue 2, pp. 1080 - 1118
We consider the inertial Qian–Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a... 
Nematic liquid crystal fluids | Navier–Stokes equations | Global wellposedness | EXISTENCE | MATHEMATICS | DE-GENNES THEORY | EQUATIONS | Navier-Stokes equations
Journal Article
Duke Mathematical Journal, ISSN 0012-7094, 2015, Volume 164, Issue 6, pp. 973 - 1040
We prove that the critical Maxwell-Klein-Gordon equation on R4+1 is globally well-posed for smooth initial data which are small in the energy norm. This... 
SPACE | MATHEMATICS | WAVE MAPS | REGULARITY | YANG-MILLS EQUATIONS | LOCAL EXISTENCE | CRITICAL SOBOLEV NORM | SCATTERING | Mathematics - Analysis of PDEs | critical MKG | 70S15 | global well-posedness | 35L70 | critical dispersive equations
Journal Article
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 01/2019, Volume 72, Issue 1, pp. 63 - 121
We study the well‐posedness theory for the MHD boundary layer. The boundary layer equations are governed by the Prandtl‐type equations that are derived from... 
ANALYTIC SOLUTIONS | SYSTEM | MATHEMATICS | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | PRANDTL EQUATIONS | NAVIER-STOKES EQUATION | HALF-SPACE | ZERO VISCOSITY LIMIT | ILL-POSEDNESS | EULER | FLOW | Boundary layer
Journal Article
Nonlinear Analysis: Real World Applications, ISSN 1468-1218, 10/2017, Volume 37, pp. 249 - 286
The purpose of this paper is to study well-posedness of the initial value problem (IVP) for the inhomogeneous nonlinear Schrödinger equation (INLS)... 
Local well-posedness | Global well-posedness | Inhomogeneous nonlinear Schrödinger equation | EXISTENCE | Inhomogeneous nonlinear | MATHEMATICS, APPLIED | WAVES | Schrodinger equation | SOLITONS | STABILITY | CAUCHY-PROBLEM | BLOW-UP SOLUTIONS | SCATTERING
Journal Article
Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 347, pp. 619 - 676
We consider the Cauchy problem for the defocusing cubic nonlinear Schrödinger equation in four space dimensions and establish almost sure local well-posedness... 
Almost sure scattering | Nonlinear Schrödinger equation | Almost sure well-posedness | Random initial data | MATHEMATICS | BENJAMIN-ONO-EQUATION | INVARIANT-MEASURES | WAVE EQUATION | GLOBAL EXISTENCE | MAPS | REGULARITY | Nonlinear Schrodinger equation | DATA CAUCHY-THEORY
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 07/2017, Volume 263, Issue 2, pp. 1419 - 1450
We prove a Prodi–Serrin-type global regularity condition for the three-dimensional Magnetohydrodynamic-Boussinesq system (3D MHD-Boussinesq) without thermal... 
Magnetohydrodynamic equations | Boussinesq equations | Partial viscosity | Regularity | Prodi–Serrin | Inviscid | EXISTENCE | ONE VELOCITY | GLOBAL REGULARITY | BLOW-UP CRITERION | GRADIENT | UNIQUENESS | MATHEMATICS | NAVIER-STOKES EQUATIONS | THEOREMS | PARTIAL DISSIPATION | Prodi-Serrin | FLOWS
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 08/2018, Volume 173, pp. 164 - 179
We consider the nonlinear stability of the Timoshenko–Cattaneo system in the one-dimensional whole space. The Timoshenko system consists of two coupled wave... 
Timoshenko systems | Regularity-loss | Cattaneo’s law | Global existence | Decay estimate | Cattaneo's law | EXISTENCE | MATHEMATICS, APPLIED | 2ND SOUND | PROPERTY | STABILITY | TRANSVERSE VIBRATIONS | MATHEMATICS | MEMORY | BARS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 2012, Volume 252, Issue 3, pp. 2698 - 2724
We prove the global well-posedness for the 3-D micropolar fluid system in the critical Besov spaces by making a suitable transformation of the solutions and... 
Highly oscillating | Littlewood–Paley decomposition | Global well-posedness | Besov space | Micropolar fluid | Littlewood-Paley decomposition | EXISTENCE | MATHEMATICS | THEOREM | EQUATIONS | UNIQUENESS | Mathematics - Analysis of PDEs
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 09/2016, Volume 142, pp. 112 - 133
Journal Article
ZAMM ‐ Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, ISSN 0044-2267, 06/2019, Volume 99, Issue 6, pp. e201700306 - n/a
In this paper, we mainly study the Cauchy problem of the tropical climate model in negative‐order Besov spaces. By using the iterative scheme and compactness... 
global existence | 35Q35 | well‐posedness | 76D03 | 35Q30 | Besov spaces | tropical climate model | EXISTENCE | MATHEMATICS, APPLIED | MECHANICS | well-posedness | EQUATIONS | CRITICAL SPACES | Climate | Analysis | Climate models | Function space | Iterative methods | Cauchy problem
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 2006, Volume 233, Issue 1, pp. 60 - 91
Journal Article