Remarks on the Prandtl Equation
Analysis of PDEs
2016-11-25 v1
Abstract
In a recent result of Gerard-Varet and Dormy [5], they established ill-posedness for the Cauchy problem of the linearized Prandtl equation around non-monotic special solution which is independent of x and satisfies the heat equation. In [6] and [7], some nonlinear ill-posedness were established with this counterexample. Then it is natural to consider the problem that does this linear ill-posedness happen whenever the non-degenerate critical points appear. In this paper, we concern the linearized Prandtl equation around general stationary solutions with non-degenerate critical points depending on x which could be considered as the time-periodic solutions and show some ill-posdness.
Keywords
Cite
@article{arxiv.1108.1269,
title = {Remarks on the Prandtl Equation},
author = {Ding Yutao},
journal= {arXiv preprint arXiv:1108.1269},
year = {2016}
}