Radially symmetric stationary wave for two-dimensional Burgers equation

Huijiang Zhao; Qingsong Zhao

doi:10.3934/dcds.2020357

Article Contents

2021, Volume 41, Issue 5: 2167-2185. Doi: 10.3934/dcds.2020357

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Radially symmetric stationary wave for two-dimensional Burgers equation

Huijiang Zhao^1,2, and
Qingsong Zhao^1,

1.
School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
2.
Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China

Received: June 30, 2020

Early access: October 2020

Published: May 2021

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Abstract

We are concerned with the radially symmetric stationary wave for the exterior problem of two-dimensional Burgers equation. A sufficient and necessary condition to guarantee the existence of such a stationary wave is given and it is also shown that the stationary wave satisfies nice decay estimates and is time-asymptotically nonlinear stable under radially symmetric initial perturbation.

Keywords:

Radially stationary wave,
Burgers equation,
exterior problem,
time-asymptotically nonlinear stability.

Mathematics Subject Classification: Primary: 35A01; Secondary: 35B40, 35K59, 37K40.

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References

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