Continuity properties of the data-to-solution map and ill-posedness for a two-component Fornberg-Whitham system

2021/07/03 by Fei, Xu, Yong, Zhang, Li, Fengquan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2107.01357

Abstract

This work studies a two-component Fornberg-Whitham (FW) system, which can be considered as a model for the propagation of shallow water waves. It's known that its solutions depend continuously on their initial data from the local well-posedness result. In this paper, we further show that such dependence is not uniformly continuous in H^s(R)× H^s-1(R) for s>(3)/(2), but Höler continuous in a weaker topology. Besides, we also establish that the FW system is ill-posed in the critical Sobolev space H^(3)/(2)(R)× H^(1)/(2)(R) by proving the norm inflation.

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