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arXiv · 1805.05229

The initial-boundary value problem for the Kawahara equation on the half-line

Márcio Cavalcante·Chulkwang Kwak
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Abstract

This paper concerns the initial-boundary value problem (IBVP) of the Kawahara equation posed on the right and left half-lines. We prove the local well-posedness in the low regularity Sobolev space. We introduce the Duhamel boundary forcing operator, which is introduced by Colliander - Kenig \cite{CK} in the context of Airy group operators, to construct solutions on the whole line. We also give the bilinear estimate in $X^{s,b}$ space for $b < \frac12$, which is almost sharp compared to IVP of Kawahara equation \cite{CLMW2009, JH2009}.

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Márcio Cavalcante, Chulkwang Kwak. 2018-05-14. The initial-boundary value problem for the Kawahara equation on the half-line. https://arxiv.org/abs/1805.05229

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