A note on the Ostrovsky equation in weighted Sobolev spaces

Abstract

In this work we consider the initial value problem (IVP) associated to the Ostrovsky equations $$\begin{array}{rl}{u}_t+{\partial }_x^{3}u\pm {\partial }_x^{-1}u+u{\partial }_{x}u& =0,x\in \mathbb{R},t\in \mathbb{R},\\ u(x,0)& =u_0(x).\end{array}\}$$ We study the well-posedness of the IVP in the weighted Sobolev spaces $$Z_{s,\frac{s}{2}}:=\{u\in H^s(\mathbb{R}):D_x^{-s}u\in L^2(\mathbb{R})\}\cap L^2(|x{|}^{s}dx),$$ with $\frac{3}{4}<s\le 1$.

arXiv admin note: text overlap with arXiv:1412.3155