Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure

Federico Cacciafesta; Anne-Sophie de Suzzoni

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arXiv · 1304.3005

Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure

Federico Cacciafesta·Anne-Sophie de Suzzoni

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Abstract

In this paper, we prove the continuity of the flow of KdV on spaces of probability measures with respect to a combination of Wasserstein distances on $H^s$, $s>0$ and $L^2$. We are motivated by the existence of an invariant measure belonging to the spaces onto which these distances are defined.

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Federico Cacciafesta, Anne-Sophie de Suzzoni. 2013-04-10. Continuity of the flow of KdV with regard to the Wasserstein metrics and application to an invariant measure. https://arxiv.org/abs/1304.3005

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