Blow up of fractional Schrödinger equations on manifolds with nonnegative Ricci curvature

Autor:	Huali Zhang, Shiliang Zhao
Rok vydání:	2020
Předmět:	symbols.namesake Weight function Mathematics - Analysis of PDEs 35A01 General Mathematics Mathematics::Analysis of PDEs General Engineering symbols Ricci curvature Heat kernel Schrödinger equation Mathematical physics Mathematics
Zdroj:	Mathematical Methods in the Applied Sciences.
ISSN:	1099-1476 0170-4214
Popis:	In this paper, the well-posedness of Cauchy's problem of fractional Schr\"odinger equations with a power type nonlinearity on $n$-dimensional manifolds with nonnegative Ricci curvature is studied. Under suitable volume conditions, the local solution with initial data in $H^{[\frac{n}{2}]+1}$ will blow up in finite time no matter how small the initial data is, which follows from a new weight function and ODE inequalities. Moreover, the upper-bound of the lifespan can be estimated. Comment: 15 pages. Welcome all comments
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a7cbf67e60f4e9392643bc5d06ff8518 https://doi.org/10.1002/mma.6490 Zobrazit plný text záznamu Plný text