On the Cauchy problem associated to a regularized Benjamin-Ono--Zakharov-Kuznetsov (rBO-ZK) type equation
Analysis of PDEs
2018-11-29 v1
Abstract
In this work we shall study the well-posedness and ill-posedness of the Cauchy problem associated to the equation \begin{equation*} u_{t}+a(u^{n})_{x}+(b\mathscr{H} u_{t}+u_{yy})_{x}=0, \end{equation*} in anisotropic weigthed Sobolev spaces. In particular, we examine the unique continuation property for solutions, of this, with polynomial decay.
Keywords
Cite
@article{arxiv.1811.11447,
title = {On the Cauchy problem associated to a regularized Benjamin-Ono--Zakharov-Kuznetsov (rBO-ZK) type equation},
author = {Fabián Sánchez S. and Félix H. Soriano M.},
journal= {arXiv preprint arXiv:1811.11447},
year = {2018}
}