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arXiv · 2305.05102

The lifespan of small data solutions for Intermediate Long Wave equation (ILW)

Mihaela Ifrim·Jean-Claude Saut
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Abstract

This article represents a first step toward understanding the long-time dynamics of solutions for the Intermediate Long Wave equation (ILW). While this problem is known to be both completely integrable and globally well-posed in $H^{\frac{3}{2}}$, much less seems to be known concerning its long-time dynamics. Here we prove well-posedness at much lower regularity, namely an $L^2$ global well-posedness result. Then we consider the case of small and localized data and show that the solutions disperse up to cubic timescale.

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Mihaela Ifrim, Jean-Claude Saut. 2023-05-09. The lifespan of small data solutions for Intermediate Long Wave equation (ILW). https://arxiv.org/abs/2305.05102

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