We study the time of existence of the solutions of the following Schrödinger equation iψt=(−Δ)sψ+f(|ψ|2)ψ,x∈Sd , or x∈Td where (−Δ)s stands for the spectrally defined fractional Laplacian with s>1/2 and f a smooth function. We prove an almost global existence result for almost all s>1/2.
Almost global existence for a fractional Schrödinger equation on spheres and tori / D. Bambusi, Y. Sire. - In: DYNAMICS OF PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 1548-159X. - 10:2(2013), pp. 171-176. [10.4310/DPDE.2013.v10.n2.a3]
Almost global existence for a fractional Schrödinger equation on spheres and tori
D. Bambusi;
2013
Abstract
We study the time of existence of the solutions of the following Schrödinger equation iψt=(−Δ)sψ+f(|ψ|2)ψ,x∈Sd , or x∈Td where (−Δ)s stands for the spectrally defined fractional Laplacian with s>1/2 and f a smooth function. We prove an almost global existence result for almost all s>1/2.
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