CPAA
Global well-posedness for the Kawahara equation with low regularity
Takamori Kato
Communications on Pure & Applied Analysis 2013, 12(3): 1321-1339 doi: 10.3934/cpaa.2013.12.1321
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.
keywords: Kawahara equation Fourier restriction norm method Cauchy problem global well-posedness I-method low regularity.

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