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arXiv · 1511.00564

The stochastic logarithmic Schr\"odinger equation

Viorel Barbu·Michael Röckner·Deng Zhang
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Abstract

In this paper we prove global existence and uniqueness of solutions to the stochastic logarithmic Schr\"odinger equation with linear multiplicative noise. Our approach is mainly based on the rescaling approach and the method of maximal monotone operators. In addition, uniform estimates of solutions in the energy space $H^1(\mathbb{R}^d)$ and in an appropriate Orlicz space are also obtained here.

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Viorel Barbu, Michael Röckner, Deng Zhang. 2015-11-02. The stochastic logarithmic Schr\"odinger equation. https://arxiv.org/abs/1511.00564

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