Homogenization for the cubic nonlinear Schr\"odinger equation on $\mathbb R^2$

Maria Ntekoume

Homogenization for the cubic nonlinear Schr\"odinger equation on $\mathbb R^2$

Analysis of PDEs 2019-11-13 v2

Authors: Maria Ntekoume

Abstract

We study the defocusing inhomogeneous mass-critical nonlinear Schr\"odinger equation on $\mathbb R^2$ $i u_t +\Delta u=g(nx) |u|^2 u$ for initial data in $L^2(\mathbb R^2)$ . We obtain sufficient conditions on $g$ to ensure existence and uniqueness of global solutions for $n$ sufficiently large, as well as homogenization.

Keywords

nonlinear schrödinger equation nonlinear schrödinger equations nonlinear schrodinger equations

Cite

@article{arxiv.1806.05778,
  title  = {Homogenization for the cubic nonlinear Schr\"odinger equation on $\mathbb R^2$},
  author = {Maria Ntekoume},
  journal= {arXiv preprint arXiv:1806.05778},
  year   = {2019}
}

Comments

25 pages

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