%0 Journal Article
%T Instabilities for supercritical Schr£żdinger equations in analytic manifolds
%A Laurent Thomann
%J Mathematics
%D 2007
%I arXiv
%X In this paper we consider supercritical nonlinear Schr\"odinger equations in an analytic Riemannian manifold $(M^d,g)$, where the metric $g$ is analytic. Using an analytic WKB method, we are able to construct an Ansatz for the semiclassical equation for times independent of the small parameter. These approximate solutions will help to show two different types of instabilities. The first is in the energy space, and the second is an immediate loss of regularity in higher Sobolev norms.
%U http://arxiv.org/abs/0707.1785v1