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arXiv · 1211.6928

Lifespan of solutions for the nonlinear Schr\"odinger equation without gauge invariance

Masahiro Ikeda
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Abstract

We study the lifespan of solutions for the nonlinear Schr\"odinger equation id_{t}u+{\Delta}u={\lambda}|u|^{p}, (t,x)\in[0,T)\timesR^{n}, with the initial condition, where 1<p\leq 1+2/n and {\lambda}\in C. Our main aim in this paper is to prove an upper bound of the lifespan in the subcritical case 1<p<1+2/n.

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Masahiro Ikeda. 2012-11-29. Lifespan of solutions for the nonlinear Schr\"odinger equation without gauge invariance. https://arxiv.org/abs/1211.6928

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