Global well-posedness for the Navier–Stokes–Nernst–Planck–Poisson system in dimension two

A Remark on Persistence of Global Well-Posedness for the Boussinesq System with Non-homogeneous Boundary in Dimension Two

A ug 2 00 8 Low regularity global well - posedness for the two - dimensional Zakharov system ∗

The two-dimensional Zakharov system is shown to have a unique global solution for data without finite energy if the L-norm of the Schrödinger part is small enough. The proof uses a refined I-method originally initiated by Colliander, Keel, Staffilani, Takaoka and Tao. A polynomial growth bound for the solution is also given.

Global Well-posedness for Euler-boussinesq System with Critical Dissipation

In this paper we study a fractional diffusion Boussinesq model which couples the incompressible Euler equation for the velocity and a transport equation with fractional diffusion for the temperature. We prove global well-posedness results.

Global Well-posedness below the Charge Norm for the Dirac-klein-gordon System in One Space Dimension

We prove global well-posedness below the charge norm (i.e., the L 2 norm of the Dirac spinor) for the Dirac-Klein-Gordon system of equations (DKG) in one space dimension. Adapting a method due to Bourgain, we split off the high frequency part of the initial data for the spinor, and exploit nonlinear smoothing effects to control the evolution of the high frequency part. To prove the nonlinear sm...

On global well/ill-posedness of the Euler-Poisson system

We discuss the problem of well-posedness of the Euler-Poisson system arising, for example, in the mathematical theory of semi-conductors, models of plasma and gaseous stars in astrophysics. We introduce the concept of dissipative weak solution satisfying, in addition to the standard system of integral identities replacing the original system of partial differential equations, the balance of tot...