Low regularity solutions for a 2D quadratic non-linear Schr\"odinger equation

Ioan Bejenaru; Daniela De Silva

Low regularity solutions for a 2D quadratic non-linear Schr\"odinger equation

Analysis of PDEs 2007-05-23 v1

Authors: Ioan Bejenaru , Daniela De Silva

Abstract

We establish that the initial value problem for the quadratic non-linear Schr\"odinger equation $iu_t - \Delta u = u^2$ where $u: \R^2 \times \R \to \C$ , is locally well-posed in $H^s(\R^2)$ when $s > -1$ . The critical exponent for this problem is $s_c=-1$ and previous work in \cite{c1} established local well-posedness for $s > -3/4$ .

Keywords

nonlinear schrödinger equations nonlinear schrodinger equations nonlinear schrödinger equation

Cite

@article{arxiv.math/0609241,
  title  = {Low regularity solutions for a 2D quadratic non-linear Schr\"odinger equation},
  author = {Ioan Bejenaru and Daniela De Silva},
  journal= {arXiv preprint arXiv:math/0609241},
  year   = {2007}
}

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