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arXiv · 2308.15814

The logarithmic Schr{\"o}dinger equation with spatial white noise on the full space

Quentin Chauleur·Antoine Mouzard
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Abstract

We solve the Schr{\"o}dinger equation with logarithmic nonlinearity and multiplicative spatial white noise on R d with d $\le$ 2. Because of the nonlinearity, the regularity structures and the paracontrolled calculus can not be used. To solve the equation, we rely on an exponential transform that has proven useful in the context of other singular SPDEs.

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Quentin Chauleur, Antoine Mouzard. 2023-08-30. The logarithmic Schr{\"o}dinger equation with spatial white noise on the full space. https://arxiv.org/abs/2308.15814

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