Lifespan of solutions for the nonlinear Schr\"odinger equation without gauge invariance
classification
🧮 math.AP
keywords
lifespanequationlambdanonlinearodingerschrsolutionsbound
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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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