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arXiv · 1207.2033

Necessary conditions and sufficient conditions for global existence in the nonlinear Schrödinger equation

Pascal Bégout
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Abstract

In this paper, we consider the nonlinear Schrödinger equation with the super critical power of nonlinearity in the attractive case. We give a sufficient condition and a necessary condition to obtain global or blowing up solutions. These conditions coincide in the critical case, thereby extending the results of Weinstein. Furthermore, we improve a blow-up condition.

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Pascal Bégout. 2012-07-09. Necessary conditions and sufficient conditions for global existence in the nonlinear Schrödinger equation. https://arxiv.org/abs/1207.2033

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