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arXiv · 1809.06685

Nonlinear Schr\"odinger equation with Coulomb potential

Changxing Miao·Junyong Zhang·Jiqiang Zheng
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Abstract

In this paper, we study the Cauchy problem for the nonlinear Schr\"odinger equations with Coulomb potential $i\partial_tu+\Delta u+\frac{K}{|x|}u=\lambda|u|^{p-1}u$ with $1 0$ and scattering theory when the Coulomb potential is repulsive i.e. $K\leq0$. The argument is based on the interaction Morawetz-type inequalities and the equivalence of Sobolev norms.

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Changxing Miao, Junyong Zhang, Jiqiang Zheng. 2018-09-18. Nonlinear Schr\"odinger equation with Coulomb potential. https://doi.org/10.1007/s10473-022-0606-x

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