On global large energy solutions to the viscous shallow water equations

Xiaoping Zhai; Hailong Ye

doi:10.3934/dcdsb.2020097

Article Contents

2020, Volume 25, Issue 11: 4277-4293. Doi: 10.3934/dcdsb.2020097

This issue Previous Article Extension, embedding and global stability in two dimensional monotone maps Next Article On the approaching time towards the attractor of differential equations perturbed by small noise

On global large energy solutions to the viscous shallow water equations

Xiaoping Zhai^1, and
Hailong Ye^1,2, ,

1.
School of Mathematics and Statistics, Shenzhen University, Shenzhen 518060, China
2.
Shenzhen Key Laboratory of Advanced Machine Learing and Applications, Shenzhen University, Shenzhen, 518060, China

^* Corresponding author: Hailong Ye
^* Corresponding author: Hailong Ye

Received: July 2011

Early access: April 2020

Published: November 2020

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Abstract

By exploring the smooth effect of the heat flows and the weighted-Chemin-Lerner technique, we obtain the global solutions of large energy to the viscous shallow water equations with initial data in the critical Besov spaces, which improves the previous small energy type arguments [5], [13]. Moreover, the method used here is quiet different from [5], [13].

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Mathematics Subject Classification: Primary: 35Q35, 76N10; Secondary: 35B40.

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References

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