Instabilities for supercritical Schrödinger equations in analytic manifolds

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dc.creatorThomann, Laurent
dc.date2007-07-12
dc.date.accessioned2026-07-07T08:16:14Z
dc.date.available2026-07-07T08:16:14Z
dc.descriptionIn 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.
dc.description31 pages
dc.identifierhttps://arxiv.org/abs/0707.1785
dc.identifierhttp://arxiv.org/abs/0707.1785
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/133712
dc.subjectAnalysis of PDEs
dc.subjectMathematical Physics
dc.subject35A07; 35A10; 35B33; 35B35; 35Q55; 81Q05
dc.titleInstabilities for supercritical Schrödinger equations in analytic manifolds
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