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arXiv · 1112.4657

The Korteweg-de-Vries equation at H^{-1} regularity

Tristan Buckmaster·Herbert Koch
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Abstract

In this paper we will prove the existence of weak solutions to the Korteweg-de Vries initial value problem on the real line with H^{-1} initial data; moreover, we will study the problem of orbital and asymptotic H^{s} stability of solitons for integers s\ge -1; finally, we will also prove new a priori H^{-1} bounds for solutions to the Korteweg-de Vries equation. The paper will utilise the Miura transformation to link the Korteweg-de Vries equation to the modified Korteweg-de Vries equation.

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Tristan Buckmaster, Herbert Koch. 2012-07-17. The Korteweg-de-Vries equation at H^{-1} regularity. https://arxiv.org/abs/1112.4657

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