On the Cauchy problem for the nonlinear semi-relativistic equation in Sobolev spaces
Analysis of PDEs
2017-10-16 v2
Abstract
We proved the local well-posedness for the power-type nonlinear semi-relativistic or half-wave equation (NLHW) in Sobolev spaces. Our proofs mainly bases on the contraction mapping argument using Strichartz estimate. We also apply the technique of Christ-Colliander- Tao in \cite{ChristCollianderTao} to prove the ill-posedness for (NLHW) in some cases of the super-critical range.
Keywords
Cite
@article{arxiv.1701.00852,
title = {On the Cauchy problem for the nonlinear semi-relativistic equation in Sobolev spaces},
author = {Van Duong Dinh},
journal= {arXiv preprint arXiv:1701.00852},
year = {2017}
}
Comments
Revised Version, To appear in Discrete Contin. Dyn. Syst. A (2018)