The lifespan of small data solutions for Intermediate Long Wave equation (ILW)
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2023
- DOI:
- 10.48550/arXiv.2305.05102
- arXiv:
- arXiv:2305.05102
- Bibcode:
- 2023arXiv230505102I
- Keywords:
-
- Mathematics - Analysis of PDEs
- E-Print:
- 42 pages. arXiv admin note: text overlap with arXiv:1701.08476, fixed typos