Well-posedness and global existence of 2D viscous shallow water system in Besov spaces

2014/02/20 by Yanan Liu, Zhaoyang Yin, Liu, Yanan +1 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1402.4923

arxiv created 2014/11/27 · arxiv updated 2014/12/01

Abstract

In this paper we consider the Cauchy problem for 2D viscous shallow water system in Besov spaces. We firstly prove the local well-posedness of this problem in B^s_p,r(ℝ²), s>max\1,(2)/(p)\, 1≤ p,r≤ ∞ by using the Littlewood-Paley theory, the Bony decomposition and the theories of transport equations and transport diffusion equations. Then we can prove the global existence of the system with small enough initial data in B^s_p,r(ℝ²), 1≤ p≤2, 1≤ r<∞ and s>(2)/(p). Our obtained results generalize and cover the recent results in \citeW.

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• Global existence and well-posedness of 2D viscous shallow water system in Sobolev spaces with low regularity

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