An Improvement on the Br\'ezis-Gallou\"et technique for 2D NLS and 1D half-wave equation

Tohru Ozawa; Nicola Visciglia

An Improvement on the Br\'ezis-Gallou\"et technique for 2D NLS and 1D half-wave equation

Analysis of PDEs 2014-03-31 v1 Mathematical Physics math.MP

Authors: Tohru Ozawa , Nicola Visciglia

Abstract

We revise the classical approach by Br\'ezis-Gallou\"et to prove global well posedness for nonlinear evolution equations. In particular we prove global well--posedness for the quartic NLS posed on general domains $\Omega$ in $\R^2$ with initial data in $H^2(\Omega)\cap H^1_0(\Omega)$ , and for the quartic nonlinear half-wave equation on $\R$ with initial data in $H^1(\R)$ .

Keywords

Brezis-Gallouet technique global well-posedness nonlinear Schrödinger equation half-wave equation quartic nonlinearity Sobolev spaces

Cite

@article{arxiv.1403.7443,
  title  = {An Improvement on the Br\'ezis-Gallou\"et technique for 2D NLS and 1D half-wave equation},
  author = {Tohru Ozawa and Nicola Visciglia},
  journal= {arXiv preprint arXiv:1403.7443},
  year   = {2014}
}

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