Global well-posedness for the Kawahara equation with low regularity

Takamori Kato

doi:10.3934/cpaa.2013.12.1321

Article Contents

2013, Volume 12, Issue 3: 1321-1339. Doi: 10.3934/cpaa.2013.12.1321

This issue Previous Article The regularity for a class of singular differential equations Next Article On the hyperbolicity and causality of the relativistic Euler system under the kinetic equation of state

Global well-posedness for the Kawahara equation with low regularity

Takamori Kato^1,

1.
Department of Mathematics, Kyoto University, Kyoto, 606-8502

Received: March 2012

Revised: July 2012

Published: May 2013

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Abstract

We consider the global well-posedness for the Cauchy problem of the Kawahara equation which is one of fifth order KdV type equations. We first establish the local well-posedness in a more suitable function space for the global well-posedness by a variant of the Fourier restriction norm method introduced by Bourgain. Next, we extend this local solution globally in time by the I-method. In the present paper, we can apply the I-method to the modified Bourgain space in which the structure of the nonlinear term is reflected.

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Mathematics Subject Classification: 35Q55.

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