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

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

2011-12-20

arxiv.org/abs/1112.4657v1

Mathematics

Analysis of PDEs

17 pages

Scientific paper

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, assuming a numerically verified condition, we will study the problem of H^{-1} stability of solitons; 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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