On The Cauchy Problem for the elliptic Zakharov-Schulman system in dimensions 2 and 3

Filipe Oliveira; Mahendra Panthee; Jorge Drumond Silva

On The Cauchy Problem for the elliptic Zakharov-Schulman system in dimensions 2 and 3

Analysis of PDEs 2011-06-27 v3

Authors: Filipe Oliveira , Mahendra Panthee , Jorge Drumond Silva

Abstract

We prove that the Cauchy problem associated to the Zakharov-Schulman system $iu_t+L_1u=uv$ , $L_2v=L_3(|u|^2)$ is locally well-posed for given initial data in Sobolev spaces $H^s(R^n)$ , $s\geq n/4$ , for n =2,3. Here, L_j denote second order operators, with L_1 non-degenerate and L_2 elliptic.

Keywords

cauchy problem zakharov-schulman system elliptic operator sobolev space local well-posedness nonlinear schrödinger equation

Cite

@article{arxiv.1002.0866,
  title  = {On The Cauchy Problem for the elliptic Zakharov-Schulman system in dimensions 2 and 3},
  author = {Filipe Oliveira and Mahendra Panthee and Jorge Drumond Silva},
  journal= {arXiv preprint arXiv:1002.0866},
  year   = {2011}
}

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