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arXiv · 2203.05374

Logarithmic Schr\"odinger Equations in Infinite Dimensions

Larry Read·Boguslaw Zegarlinski·Mengchun Zhang
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Abstract

We study the logarithmic Schr\"odinger equation with finite range potential on $\mathbb{R}^{\mathbb{Z}^d}$. Through a ground-state representation, we associate and construct a global Gibbs measure and show that it satisfies a logarithmic Sobolev inequality. We find estimates on the solutions in arbitrary dimension and prove the existence of weak solutions to the infinite-dimensional Cauchy problem.

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Larry Read, Boguslaw Zegarlinski, Mengchun Zhang. 2022-03-10. Logarithmic Schr\"odinger Equations in Infinite Dimensions. https://doi.org/10.1063/5.0102156

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