Global well-posedness for the two-dimensional Maxwell-Navier-Stokes equations

Abstract

In this paper, we investigate Cauchy problem of the two-dimensional full Maxwell-Navier-Stokes system, and prove the global-in-time existence and uniqueness of solution in the borderline space which is very close to $L^2$-energy space by developing the new estimate of ${\sup }_{j\in \mathbb{Z}}{2}^{2j}{\int }_0^t{\sum }_{k\in {\mathbb{Z}}^2}\Vert \sqrt{{\varphi }_{i,k}}u(\tau ){\Vert }_{L^2({\mathbb{R}}^2)}^2\text{d}\tau <\infty$. This solves the open problem in the framework of borderline space purposed by Masmoudi in \cite{Masmoudi-10}.

46pages

References in corpus (1)

• On the global wellposedness of the 3-D Navier-Stokes equations with large initial data