Stabilization of Dispersion Generalized Benjamin Ono
Analysis of PDEs
2017-10-02 v1
Abstract
In this article, we examine well-posedness and stabilization property of the dispersion-generalized Benjamin-Ono equation with periodic boundary conditions. The main ingredient of our proof is a development of dissipation-normalized Bourgain space, which gains smoothing properties simultaneously from dissipation and dispersion within the equation. We will establish a bilinear estimate for the derivative nonlinearity using this space and prove the linear observability inequality leading to small-data stabilization.
Cite
@article{arxiv.1709.10224,
title = {Stabilization of Dispersion Generalized Benjamin Ono},
author = {Cynthia Flores and Seungly Oh and Derek Smith},
journal= {arXiv preprint arXiv:1709.10224},
year = {2017}
}