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arXiv · 1812.06661

Decay of the stochastic linear Schrödinger equation in $d \geq 3$ with small multiplicative noise

Chenjie Fan·Weijun Xu
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Abstract

We give decay estimates of the solution to the linear Schrödinger equation in dimension $d \geq 3$ with a small noise which is white in time and colored in space. As a consequence, we also obtain certain asymptotic behaviour of the solution. The proof relies on the bootstrapping argument used by Journé-Soffer-Sogge for decay of deterministic Schrödinger operators.

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Chenjie Fan, Weijun Xu. 2018-12-17. Decay of the stochastic linear Schrödinger equation in $d \geq 3$ with small multiplicative noise. https://arxiv.org/abs/1812.06661

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