An improved bilinear estimate for Benjamin-Ono type equations
Analysis of PDEs
2009-04-06 v1
Abstract
A bilinear estimate in Fourier restriction norm spaces with applications to the Cauchy problem associated to u_t - |D|^{\alpha}u_x + uu_x =0 is proved, for 1< \alpha <2. As a consequence, local well-posedness in H^s(\R) \cap \dot{H}^{-\omega}(\R) follows for s >-{3/4}(\alpha-1) and \omega=1/\alpha-1/2. This extends to global well-posedness for all s \geq 0.
Cite
@article{arxiv.math/0509218,
title = {An improved bilinear estimate for Benjamin-Ono type equations},
author = {S. Herr},
journal= {arXiv preprint arXiv:math/0509218},
year = {2009}
}