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arXiv · 2103.13214

Finite time/Infinite time blow-up behaviors for the inhomogeneous nonlinear Schr\"{o}dinger equation

Ruobing Bai·Bing Li
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Abstract

In this work, we consider the following focusing inhomogeneous nonlinear Schr\"odinger equation \begin{align*} i\partial_t u+\Delta u +|x|^{-b}|u|^p u=0,\quad (t, x)\in\mathbb{R}\times\mathbb{R}^N \end{align*} with $0 0. \end{equation*} To our knowledge, the statement (1) establishes the first finite time blow-up result for this equation in the intercritical case when the initial data $u_0$ doesn't have finite variance and is non-radial. The statement (2) gives the first result for the infinite time blow-up rate for this equation.

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Ruobing Bai, Bing Li. 2021-03-24. Finite time/Infinite time blow-up behaviors for the inhomogeneous nonlinear Schr\"{o}dinger equation. https://arxiv.org/abs/2103.13214

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