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arXiv · 1808.06494

Local well-posedness of the fifth-order KdV-type equations on the half-line

Márcio Cavalcante·Chulkwang Kwak
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Abstract

This paper is a continuation of authors' previous work \cite{CK2018-1}. We extend the argument \cite{CK2018-1} to fifth-order KdV-type equations with different nonlinearities, in specific, where the scaling argument does not hold. We establish the $X^{s,b}$ nonlinear estimates for $b < \frac12$, which is almost optimal compared to the standard $X^{s,b}$ nonlinear estimates for $b > \frac12$ \cite{CGL2010, JH2009}. As an immediate conclusion, we prove the local well-posedness of the initial-boundary value problem (IBVP) for fifth-order KdV-type equations on the right half-line and the left half-line.

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Márcio Cavalcante, Chulkwang Kwak. 2018-08-16. Local well-posedness of the fifth-order KdV-type equations on the half-line. https://arxiv.org/abs/1808.06494

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