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arXiv · 1610.06901

Global well-posedness and blow-up on the energy space for the Inhomogeneous Nonlinear Schr\"odinger Equation

Luiz Gustavo Farah
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Abstract

We consider the supercritical inhomogeneous nonlinear Schr\"odinger equation (INLS) $$i\partial_t u+\Delta u+|x|^{-b}|u|^{2\sigma}u=0,$$ where $(2-b)/N<\sigma<(2-b)/(N-2)$ and $0<b<\min\{2,N\}$. We prove a Gagliardo-Nirenberg type estimate and use it to establish sufficient conditions for global existence and blow-up in $H^1(\mathbb{R}^N)$.

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Luiz Gustavo Farah. 2016-10-21. Global well-posedness and blow-up on the energy space for the Inhomogeneous Nonlinear Schr\"odinger Equation. https://arxiv.org/abs/1610.06901

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