Gevrey class smoothing effect for the Prandtl equation
Analysis of PDEs
2015-05-28 v3
Abstract
It is well known that the Prandtl boundary layer equation is instable, and the well-posedness in Sobolev space for the Cauchy problem is an open problem. Recently, under the Oleinik's monotonicity assumption for the initial datum, [1] have proved the local well-posedness of Cauchy problem in Sobolev space (see also [21]). In this work, we study the Gevrey smoothing effects of the local solution obtained in [1]. We prove that the Sobolev's class solution belongs to some Gevrey class with respect to tangential variables at any positive time.
Cite
@article{arxiv.1502.03569,
title = {Gevrey class smoothing effect for the Prandtl equation},
author = {Weixi Li and Di Wu and Chao-Jiang Xu},
journal= {arXiv preprint arXiv:1502.03569},
year = {2015}
}