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

Yanan Liu; Zhaoyang Yin

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arXiv · 1411.0461

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

Yanan Liu·Zhaoyang Yin

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Abstract

In this paper we consider the Cauchy problem for 2D viscous shallow water system in $H^s(\mathbb{R}^2)$, $s>1$. 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 $H^s(\mathbb{R}^2)$, $s>1$. Our obtained result improves the recent result in \cite{W}

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Yanan Liu, Zhaoyang Yin. 2014-11-03. Global existence and well-posedness of 2D viscous shallow water system in Sobolev spaces with low regularity. https://arxiv.org/abs/1411.0461

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