On the initial value problem for higher dimensional Camassa-Holm equations

Kai Yan; Zhaoyang Yin

doi:10.3934/dcds.2015.35.1327

Article Contents

2015, Volume 35, Issue 3: 1327-1358. Doi: 10.3934/dcds.2015.35.1327

This issue Previous Article Equilibrium states and invariant measures for random dynamical systems Next Article Existence of weak solutions to the three-dimensional density-dependent generalized incompressible magnetohydrodynamic flows

On the initial value problem for higher dimensional Camassa-Holm equations

Kai Yan^1, and
Zhaoyang Yin^2,

1.
College of Information Science and Technology, Jinan University, Guangzhou, 510632
2.
Department of Mathematics, Zhongshan University, Guangzhou, 510275

Received: March 31, 2014

Revised: June 30, 2014

Published: February 2015

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Abstract

This paper is concerned with the the initial value problem for higher dimensional Camassa-Holm equations. Firstly, the local well-posedness for this equations in both supercritical and critical Besov spaces are established. Then two blow-up criterions of strong solutions to the equations are derived. Finally, the analyticity of its solutions is proved in both variables, globally in space and locally in time.

Keywords:

Higher dimensional Camassa-Holm equations,
initial value problem,
local well-posedness,
Besov spaces,
blow up,
analytic solutions.

Mathematics Subject Classification: Primary: 35Q35, 35Q51; Secondary: 35L30.

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