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arXiv · 1710.06477

Energy critical Schr\"odinger equation with weighted exponential nonlinearity I: Local and global well-posedness

Abdelwahab Bensouilah·Dhouha Draouil·Mohamed Majdoub
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Abstract

We investigate the initial value problem for a defocusing nonlinear Schr\"odinger equation with weighted exponential nonlinearity $$ i\partial_t u+\Delta u=\frac{u}{|x|^b}(e^{\alpha|u|^2}-1); \qquad (t,x) \in \mathbb{R}\times\mathbb{R}^2, $$ where $0< b <1$ and $\alpha=2\pi(2-b)$. We establish local and global well-posedness in the subcritical and critical regimes.

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Abdelwahab Bensouilah, Dhouha Draouil, Mohamed Majdoub. 2017-10-17. Energy critical Schr\"odinger equation with weighted exponential nonlinearity I: Local and global well-posedness. https://arxiv.org/abs/1710.06477

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