Enhanced existence time of solutions to evolution equations of Whitham type
Analysis of PDEs
2022-04-27 v2
Abstract
We show that Whitham type equations u_t + u u_x -L u_x = 0, where L is a general Fourier multiplier operator of order \alpha \in [-1,1], \alpha\neq 0, allow for small solutions to be extended beyond their expected existence time. The result is valid for a range of quadratic dispersive equations with inhomogeneous symbols in the dispersive range given by \alpha, and should be extendable to other equations of the same relative dispersive strength.
Cite
@article{arxiv.2008.12722,
title = {Enhanced existence time of solutions to evolution equations of Whitham type},
author = {Mats Ehrnström and Yuexun Wang},
journal= {arXiv preprint arXiv:2008.12722},
year = {2022}
}