Gevrey regularity for a class of dissipative equations with applications to decay

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:253

Article

Biswas, Animikh

关键词: Gevrey regularity;    Navier-Stokes equations;    Dissipative equations;    Time decay;   

DOI  :  10.1016/j.jde.2012.08.003

来源: Elsevier

【 摘 要 】

In this paper, following the techniques of Foias and Temam, we tablish Gevrey class regularity of solutions to a class of dissipative equations with a general quadratic nonlinearity and a general dissipation including fractional Laplacian. The initial data is taken to be in Besov type spaces defined via caloric extension. We apply our result to the Navier-Stokes equations, the surface quasi-geostrophic equations, the Kuramoto-Sivashinsky equation and the barotropic quasi-geostrophic equation. Consideration of initial data in critical regularity spaces allow us to obtain generalizations of existing results on the higher order temporal decay of solutions to the Navier-Stokes equations. In the 3D case, we extend the class of initial data where such decay holds while in 2D we provide a new class for such decay. Similar decay result, and uniform analyticity band on the attractor, is also proven for the sub-critical 2D surface quasi-geostrophic equation. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free