Related papers: Global solutions to the Oldroyd-B model with a cla…
The L^2 -critical defocusing nonlinear Schrodinger initial value problem on R^d is known to be locally well-posed for initial data in L^2. Hamiltonian conservation and the pseudoconformal transformation show that global well-posedness holds…
We prove global well-posedness for low regularity data for the one dimensional quintic defocusing nonlinear Schr\"odinger equation. Precisely we show that a unique and global solution exists for initial data in the Sobolev space…
We prove that for sufficiently small initial displacements in some weighted Sobolev space, the Cauchy problem of the systems of incompressible isotropic elastodynamics in two space dimensions admits a uniqueness global classical solution.
Global well-posedness of the initial-boundary value problem for the stochastic Kuramoto-Sivashinsky equation in a bounded domain $D$ with a multiplicative noise is studied. It is shown that under suitable sufficient conditions, for any…
The study of the 2D Euler equation with non Lipschitzian velocity was initiated by Yudovich in [19] where a result of global well-posedness for essentially bounded vorticity is proved. A lot of works have been since dedicated to the…
This paper is concerned with the stability and large-time behavior for 3D magneto-micropolar equations with horizontal dissipation. The global well-posedness of the aforementioned system is established, with the initial data and its…
This paper establishes a sharp characterization of temporal decay rates for the incompressible Oldroyd-B model in a critical $L^p$ framework, covering the physically relevant and mathematically delicate case where both the fluid viscosity…
This work is devoted to the study of a viscous shallow-water system with friction and capillarity term. We prove in this paper the existence of global strong solutions for this system with some choice of large initial data when $N\geq 2$ in…
The issue of global well-posedness for the 3D inhomogenous incompressible Navier-Stokes equations was first addressed by Kazhikov in 1974. In this manuscript, we obtain its global well-posedness for the system with density-dependent…
We prove the existence of global, smooth solutions to the 2D Muskat problem in the stable regime whenever the product of the maximal and minimal slopes is strictly less than 1. The curvature of these solutions solutions decays to 0 as $t$…
Local and global well-posedness results are established for the initial value problem associated to the 1D Zakharov-Rubenchik system. We show that our results are sharp in some situations by proving Ill-posedness results otherwise. The…
This paper studies the global well-posedness of the incompressible magnetohydrodynamic (MHD) system with a velocity damping term. We establish the global existence and uniqueness of smooth solutions when the initial data is close to an…
By a new energy approach involved in the high frequencies and low frequencies decomposition in the Besov spaces, we obtain the optimal decay for the incompressible Oldroyd-B model without damping mechanism in $\mathbb{R}^n$ ($n\ge 2$). More…
In this paper, we consider the initial-boundary value problem of the 3D primitive equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal momentum equations and only horizontal…
Consider the set of equations describing Oldroyd-B fluids in an exterior domain. It is shown that this set of equations admits a unique, global solution in a certain function space provided the initial data, but not necessarily the coupling…
In this paper, we consider the 3D primitive equations of oceanic and atmospheric dynamics with only horizontal eddy viscosities in the horizontal momentum equations and only vertical diffusivity in the temperature equation. Global…
The present paper is dedicated to the global well-posedness for the 3D inhomogeneous incompressible Navier-Stokes equations, in critical Besov spaces without smallness assumption on the variation of the density. We aim at extending the work…
In this paper we are concerned with the global well-posedness for the compressible MHD equations with large data. We show that if the shear viscosity $\mu$ is a positive constant and the bulk viscosity $\lambda$ is the power function of the…
We study the global well-posedness of the two-dimensional defocusing fourth-order Schr\"odinger initial value problem with power type nonlinearities $\vert u\vert^{2k}u$ where $k$ is a positive integer. By using the $I$-method, we prove…
We give a small data global well-posedness result for an incompressible Oldroyd-B model with wave number dissipation in the equation of stress tensor. The result is uniform in solvent Reynolds numbers, and requires only fractional…