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arXiv · 0707.1785

Instabilities for supercritical Schrödinger equations in analytic manifolds

Laurent Thomann
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Abstract

In this paper we consider supercritical nonlinear Schrödinger 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.

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Laurent Thomann. 2007-07-12. Instabilities for supercritical Schrödinger equations in analytic manifolds. https://arxiv.org/abs/0707.1785

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