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Journal of Differential Equations, ISSN 0022-0396, 12/2019, Volume 268, Issue 1, pp. 160 - 185
We show robustness of various truncated and subcritical approximations to the stochastic defocusing mass-critical nonlinear Schrödinger equation (NLS) in... 
MATHEMATICS | GLOBAL WELL-POSEDNESS | SCATTERING
Journal Article
Communications on Pure and Applied Mathematics, ISSN 0010-3640, 07/2016, Volume 69, Issue 7, pp. 1354 - 1396
For the physical vacuum free boundary problem with the sound speed being C1/2‐Hölder continuous near vacuum boundaries of the one‐dimensional compressible... 
MATHEMATICS | MATHEMATICS, APPLIED | WELL-POSEDNESS
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2015, Volume 259, Issue 11, pp. 5982 - 6008
In this paper, we obtain global existence and energy decay for 3D Hall-magnetohydrodynamics (Hall-MHD) system with −Δu and −ΔB. Besides the classical energy... 
Energy decay | Global well-posedness | Blow-up criteria | Hall-MHD system | MATHEMATICS | NAVIER-STOKES EQUATIONS | WELL-POSEDNESS | MAGNETOHYDRODYNAMICS | WEAK SOLUTIONS
Journal Article
JOURNAL OF DIFFERENTIAL EQUATIONS, ISSN 0022-0396, 01/2016, Volume 260, Issue 1, pp. 818 - 859
We propose a priori estimates for a weak solution to the derivative nonlinear Schrodinger equation (DNLS) on torus with small L-2-norm datum in low regularity... 
MATHEMATICS | GLOBAL WELL-POSEDNESS | Nonlinear Schrodinger equation | Well-posedness
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 01/2016, Volume 260, Issue 1, pp. 818 - 859
We propose a priori estimates for a weak solution to the derivative nonlinear Schrödinger equation (DNLS) on torus with small L2-norm datum in low regularity... 
Nonlinear Schrödinger equation | Well-posedness
Journal Article
Annals of Mathematics, ISSN 0003-486X, 5/2010, Volume 171, Issue 3, pp. 1903 - 1930
Motivated by the critical dissipative quasi-geostrophic equation, we prove that drift-diffusion equations with L² initial data and minimal assumptions on the... 
Cubes | Maximum principle | Mathematical theorems | Truncation | Cylinders | MATHEMATICS | REGULARITY | GLOBAL WELL-POSEDNESS | BEHAVIOR
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 02/2017, Volume 290, Issue 2-3, pp. 435 - 441
This paper addresses the problem of well‐posedness of non‐autonomous linear evolution equations ẋ=A(t)x in uniformly convex Banach spaces. We assume that... 
34K30 | 47D06 | 81Q99 | time‐dependent Hamiltonians | Schrödinger equations | Non‐autonomous linear evolution equations | well‐posedness | counterexamples to well‐posedness | counterexamples to well-posedness | Non-autonomous linear evolution equations | time-dependent Hamiltonians | well-posedness | MATHEMATICS | Schrodinger equations | TIME
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 10/2017, Volume 263, Issue 8, pp. 4658 - 4722
We establish the global well-posedness of the derivative nonlinear Schrödinger equation with periodic boundary condition in the Sobolev space H12, provided... 
Global well-posedness | Derivative nonlinear Schrödinger equation
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 10/2016, Volume 442, Issue 1, pp. 273 - 290
Recently, to describe the unidirectional propagation of water waves, Bona et al. [7] introduced a fifth order KdV–BBM type... 
Water wave models | KdV equation | Nonlinear dispersive wave equations | BBM equation | Local & global well-posedness | Cauchy problem | Local and global well-posedness | MATHEMATICS | MATHEMATICS, APPLIED | ENERGY SPACE | SYSTEMS | WELL-POSEDNESS | GENERALIZED KDV EQUATION | Water waves | Analysis
Journal Article
Comptes rendus - Mathématique, ISSN 1631-073X, 05/2012, Volume 350, Issue 9-10, pp. 499 - 503
In this Note we study the generalized 2D Zakharov–Kuznetsov equations ∂tu+Δ∂xu+uk∂xu=0 for k⩾2. By an iterative method we prove the local well-posedness of... 
MATHEMATICS | WELL-POSEDNESS
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, 02/2016, Volume 260, Issue 3, pp. 2225 - 2258
The asymptotic behavior of solutions to a singular chemotaxis system modeling the onset of tumor angiogenesis in two and three dimensional whole spaces is... 
Tumor angiogenesis | Decay estimates | Energy estimates | Global well-posedness | Chemotaxis | GLOBAL EXISTENCE | WELL-POSEDNESS | MHD EQUATIONS | TRAVELING-WAVES | MATHEMATICS | KELLER-SEGEL SYSTEM | NONLINEAR STABILITY | DIFFUSION | CONSERVATION-LAWS | HYPERBOLIC-PARABOLIC SYSTEM | REINFORCED RANDOM-WALKS | Analysis | Models | Tumors
Journal Article
Mathematische Nachrichten, ISSN 0025-584X, 09/2017, Volume 290, Issue 13, pp. 2052 - 2077
We show well‐posedness of the elastic flow of open curves with clamped boundary conditions. To show short time existence we prove that the linearised problem... 
35K52 | 53A04 | 53C44 | clamped boundary conditions | maximal regularity | elastic energy | Well‐posedness | Well-posedness | MATHEMATICS | BOUNDARY-CONDITIONS | REGULARITY | L-2-FLOW | STABILITY | LINE | EQUATIONS | LOCAL WELL-POSEDNESS
Journal Article
SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2017, Volume 49, Issue 3, pp. 2246 - 2268
We define and study the Cauchy problem for a one-dimensional (1-D) nonlinear Dirac equation with nonlinearities concentrated at one point. Global... 
Nonlinear Dirac equation | Point interactions | Well-posedness | MATHEMATICS, APPLIED | nonlinear Dirac equation | WAVES | NLS EQUATION | well-posedness | point interactions | FIELD | SCHRODINGER-EQUATION | CAUCHY-PROBLEM | GLOBAL WELL-POSEDNESS
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 08/2019, Volume 476, Issue 2, pp. 391 - 425
We prove that the initial value problem associated to a nonlocal perturbation of the Benjamin-Ono equation is locally and globally well-posed in Sobolev spaces... 
Benjamin-Ono equation | Sobolev spaces | Local and global well-posedness | Weighted Sobolev spaces | MATHEMATICS | MATHEMATICS, APPLIED | ZAKHAROV-KUZNETSOV EQUATION | CAUCHY-PROBLEM | SHARP WELL-POSEDNESS
Journal Article
Nonlinear Analysis, ISSN 0362-546X, 11/2019, Volume 188, pp. 50 - 69
In this work we prove that the initial value problem (IVP) associated to the two-dimensional Benjamin–Ono equation ut+HΔu+uux=0,(x,y)∈T2,t∈R,u(x,y,0)=u0(x,y),... 
Benjamin–Ono equation | Sobolev spaces | Well-posedness | MATHEMATICS | MATHEMATICS, APPLIED | Benjamin-Ono equation | GLOBAL WELL-POSEDNESS | Boundary value problems | Well posed problems | Sobolev space | Hilbert transformation | Cauchy problem
Journal Article
Journal of Differential Equations, ISSN 0022-0396, 12/2016, Volume 261, Issue 12, pp. 6950 - 6981
Consider the full primitive equations, i.e. the three dimensional primitive equations coupled to the equation for temperature and salinity, and subject to... 
Primitive equations | Global strong well-posedness
Journal Article
Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 01/2017, Volume 445, Issue 1, pp. 81 - 96
We study a new type of nonlinear Schrödinger equation where the coefficient of Laplacian depends on spatial variable. Based on a modified Hankel transform and... 
Strichartz estimate | Schrödinger equation with spatial variable coefficient | Well-posedness
Journal Article
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