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

2014/11/03 by Yanan Liu, Zhaoyang Yin, Liu, Yanan +1
Mathematics · #30H25 #35A01 #35B44 #42B25 #49K40 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations #math.AP #msc:30H25 #msc:35A01 #msc:35B44 #msc:42B25 #msc:49K40

paper · pdf · doi:10.48550/arxiv.1411.0461

arXiv admin note: substantial text overlap with arXiv:1402.4923

arxiv created 2014/11/03 · openalex publication_date 2014/11/03 · arxiv updated 2014/11/04 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In this paper we consider the Cauchy problem for 2D viscous shallow water system in H^s(ℝ²), s>1. We first prove the local well-posedness of this problem by using the Littlewood-Paley theory, the Bony decomposition, and the theories of transport equations and transport diffusion equations. Then, we get the global existence of the system with small initial data in H^s(ℝ²), s>1. Our obtained result improves the recent result in \citeW

Citations

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

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