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1994, Operator theory, advances and applications, ISBN 0817650245, Volume 69., xiv, 349
Book
Journal of Differential Equations, ISSN 0022-0396, 03/2019, Volume 266, Issue 6, pp. 2978 - 3013
In this paper, we are concerned with the motion of electrically conducting fluid governed by the two-dimensional non-isentropic viscous compressible MHD system... 
Non-monotonic velocity fields | Local well-posedness | Compressible MHD | Boundary layers | SYSTEM | GLOBAL EXISTENCE | PRANDTL EQUATIONS | ZERO VISCOSITY LIMIT | ILL-POSEDNESS | ANALYTIC SOLUTIONS | MATHEMATICS | NAVIER-STOKES EQUATION | HALF-SPACE | SPECTRAL INSTABILITY | EULER
Journal Article
SIAM Journal on Optimization, ISSN 1052-6234, 2016, Volume 26, Issue 3, pp. 1411 - 1428
In this paper, we consider the collection of unconstrained polynomial optimization problems, in which every problem of the collection is obtained by... 
Well-posed problems | Polynomial optimization | Sharp minima | Semialgebraic geometry | Nondegeneracy at infinity | well-posed problems | nondegeneracy at infinity | LOJASIEWICZ EXPONENT | MATHEMATICS, APPLIED | REPRESENTATIONS | CONVEX | GLOBAL OPTIMIZATION | polynomial optimization | sharp minima | SQUARES | semialgebraic geometry | SUMS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 06/2019, Volume 266, Issue 12, pp. 7844 - 7889
The free boundary problem for the three dimensional incompressible elastodynamics system is studied under the Rayleigh–Taylor sign condition. Both the columns... 
Elastodynamics | Incompressible | Free boundary problem | FREE-SURFACE | MATHEMATICS | MOTION | GLOBAL EXISTENCE | FLUID | STABILITY | VORTEX SHEETS | LOCAL EXISTENCE | EULER EQUATIONS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 03/2017, Volume 262, Issue 6, pp. 3488 - 3523
This paper studies the global (in time) regularity and large time behavior of solutions to the 2D micropolar equations with only angular viscosity dissipation.... 
Large-time behavior | Angular viscosity dissipation | Global well-posedness | Micropolar equation | MATHEMATICS | REGULARITY | SPACES | FLUID-FLOWS | WEAK SOLUTIONS | Control systems
Journal Article
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, ISSN 0294-1449, 10/2019
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2017, Volume 263, Issue 12, pp. 8749 - 8803
In this paper, we study the long time well-posedness for the nonlinear Prandtl boundary layer equation on the half plane. While the initial data are small... 
Monotonic condition | Energy method | Well-posedness theory | Sobolev space | Prandtl boundary layer equation | SYSTEM | GLOBAL EXISTENCE | ILL-POSEDNESS | BOUNDARY-LAYER EQUATIONS | ANALYTIC SOLUTIONS | MATHEMATICS | ZERO-VISCOSITY LIMIT | NAVIER-STOKES EQUATION | HALF-SPACE | SPECTRAL INSTABILITY | EULER | Analysis of PDEs | Mathematics
Journal Article
Annales de l'Institut Henri Poincaré / Analyse non linéaire, ISSN 0294-1449, 11/2018, Volume 35, Issue 7, pp. 1719 - 1756
We show that the Cauchy problem for a class of dispersive perturbations of Burgers' equations containing the low dispersion Benjamin–Ono equation is locally... 
Modified energy | Global well-posedness | Nonlinear dispersive equations | Benjamin–Ono type equations with low dispersion | ISSUES | MATHEMATICS, APPLIED | BENJAMIN-ONO-EQUATION | REGULARITY | INITIAL-VALUE PROBLEM | Benjamin-Ono type equations with low dispersion
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 03/2020, Volume 483, Issue 2, p. 123633
The goal of this paper is supposed to investigate the weak well-posedness for the modified Camassa-Holm equation with cubic nonlinearity after given an initial... 
Cubic nonlinearity | Camassa-Holm equation | Weak well-posedness | Flow | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | BREAKING WAVES | CAUCHY-PROBLEM | BLOW-UP | GLOBAL CONSERVATIVE SOLUTIONS | SHALLOW-WATER EQUATION
Journal Article
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 04/2020, Volume 484, Issue 1, p. 123668
In this paper, we investigate the global existence and uniqueness of strong solutions to 2D Boussinesq system with variable kinematic viscosity depending on... 
Boussinesq system | Weak dissipation | Global well-posedness | Asymptotic behavior
Journal Article
Journal of Functional Analysis, ISSN 0022-1236, 10/2016, Volume 271, Issue 8, pp. 2177 - 2214
This paper deals with the global existence and uniqueness results for the three-dimensional incompressible Euler equations with a particular structure for... 
Global existence | Helicoidal Euler equation | Uniqueness | HELICAL SYMMETRY | EXISTENCE | SPACE | MATHEMATICS | INCOMPRESSIBLE FLOWS | IDEAL FLUID | TIME | VORTICITY
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 02/2020, Volume 482, Issue 1, p. 123529
We consider the free boundary problem for the flow of an incompressible inviscid elastic fluid. The columns of the deformation gradient are tangent and the... 
Free boundary | Elastodynamics | Inviscid flows | Well-posedness | Incompressible fluids | EXISTENCE | VACUUM INTERFACE PROBLEM | MATHEMATICS, APPLIED | VORTEX SHEETS | FREE-SURFACE | MATHEMATICS | SOBOLEV SPACES | MOTION | WATER-WAVE PROBLEM | GLOBAL-SOLUTIONS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2019, Volume 478, Issue 2, pp. 1020 - 1026
Recently, by using the argument of Lei & Lin (2011) , Liu & Gao (2017) establish the global well-posedness of mild solutions to the three-dimensional... 
Global well-posedness | Boussinesq equations | Mild solutions | MATHEMATICS | MATHEMATICS, APPLIED | TIME DECAY
Journal Article
Annales de l'Institut Henri Poincaré C, Analyse non linéaire, ISSN 0294-1449, 12/2019
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 09/2019, Volume 477, Issue 2, pp. 1087 - 1113
We prove the global well-posedness of weak solutions for nonlinear wave equations with supercritical source and damping terms on a three-dimensional torus of... 
Damping | Source terms | Supercritical | Nonlinear wave equations | Global well-posedness | MATHEMATICS, APPLIED | HYPERBOLIC EQUATION | CAUCHY-PROBLEM | EVOLUTION-EQUATIONS | VISCOELASTICITY | ANALYTICITY | MATHEMATICS | NONEXISTENCE THEOREMS | SYSTEMS | BOUNDARY | BLOW-UP | WEAK SOLUTIONS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 11/2019, Volume 479, Issue 1, pp. 688 - 702
We consider the Cauchy problem associated to the recently derived higher order Hamiltonian model for unidirectional water waves and prove global existence for... 
Water wave models | KdV equation | Cauchy problems | Nonlinear dispersive wave equations | BBM equation | Local & global well-posedness | MATHEMATICS, APPLIED | MODEL | MATHEMATICS | AMPLITUDE LONG WAVES | NONLINEAR DISPERSIVE MEDIA | BOUSSINESQ EQUATIONS | SYSTEMS | WATER
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2019, Volume 268, Issue 1, pp. 141 - 159
We study the Cauchy problem for fractional Schrödinger equation with cubic convolution nonlinearity ( ) with Cauchy data in the modulation spaces . For , we... 
Fractional Hartree equation | Modulation spaces | Global well-posedness | Fourier algebra | MATHEMATICS | CAUCHY-PROBLEM | MULTIPLIERS | Algebra
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2015, Volume 47, Issue 2, pp. 1562 - 1589
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 11/2019
Journal Article
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