Nonuniform dependence on initial data for compressible gas dynamics: The periodic Cauchy problem

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:263

Article

Keyfitz, B. L.¹  Tiglay, F.² 

[1] Ohio State Univ, Dept Math, 231 West 18th Ave, Columbus, OH 43210 USA

[2] Ohio State Univ, 1179 Univ Dr, Newark, OH 43055 USA

关键词: Compressible gas dynamics;    Well-posedness;    Hyperbolic conservation laws;   

DOI  :  10.1016/j.jde.2017.07.020

来源: Elsevier

【 摘 要 】

We start with the classic result that the Cauchy problem for ideal compressible gas dynamics is locally well posed in time in the sense of Hadamard; there is a unique solution that depends continuously on initial data in Sobolev space H-s for s > d/2+1 where d is the space dimension. We prove that the data to solution map for periodic data in two dimensions although continuous is not uniformly continuous. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free