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arXiv · 2408.08825

Minimal mass blow-up solutions for a inhomogeneous NLS equation

Mykael Cardoso·Luiz Gustavo Farah
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Abstract

We consider the inhomogeneous nonlinear Schr\"odinger (INLS) equation in $\mathbb{R}^N$ \begin{align}\label{inls} i \partial_t u +\Delta u +V(x)|u|^{\frac{4-2b}{N}}u = 0, \end{align} where $V(x) = k(x)|x|^{-b}$, with $b>0$. Under suitable assumptions on $k(x)$, we established the threshold for global existence and blow-up and then study the existence and non-existence of minimal mass blow-up solutions.

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Mykael Cardoso, Luiz Gustavo Farah. 2024-08-16. Minimal mass blow-up solutions for a inhomogeneous NLS equation. https://arxiv.org/abs/2408.08825

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