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arXiv · 1606.03715

On the regularity of solutions to the $k$-generalized Korteweg-de Vries equation

Carlos E. Kenig·Felipe Linares·Gustavo Ponce·Luis Vega
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Abstract

This work is concerned with special regularity properties of solutions to the $k$-generalized Korteweg-de Vries equation. In \cite{IsazaLinaresPonce} it was established that if the initial datun $u_0\in H^l((b,\infty))$ for some $l\in\mathbb Z^+$ and $b\in \mathbb R$, then the corresponding solution $u(\cdot,t)$ belongs to $H^l((\beta,\infty))$ for any $\beta \in \mathbb R$ and any $t\in (0,T)$. Our goal here is to extend this result to the case where $\,l\in \mathbb R^+$.

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Carlos E. Kenig, Felipe Linares, Gustavo Ponce, Luis Vega. 2016-06-12. On the regularity of solutions to the $k$-generalized Korteweg-de Vries equation. https://arxiv.org/abs/1606.03715

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