1D stochastic pressure equation with log-correlated Gaussian coefficients

Benny Avelin; Tuomo Kuusi; Patrik Nummi; Eero Saksman; Jonas M. Tölle; Lauri Viitasaari

doi:10.1016/j.spa.2025.104808

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arXiv · 2402.09127

1D stochastic pressure equation with log-correlated Gaussian coefficients

Benny Avelin·Tuomo Kuusi·Patrik Nummi·Eero Saksman·Jonas M. Tölle·Lauri Viitasaari

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Abstract

We study unique solvability for one dimensional stochastic pressure equation with diffusion coefficient given by the Wick exponential of log-correlated Gaussian fields. We prove well-posedness for Dirichlet, Neumann and periodic boundary data, and the initial value problem, covering the cases of both the Wick renormalization of the diffusion and of point-wise multiplication. We provide explicit representations for the solutions in both cases, characterized by the $S$-transform and the Gaussian multiplicative chaos measure.

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Benny Avelin, Tuomo Kuusi, Patrik Nummi, Eero Saksman, Jonas M. Tölle, Lauri Viitasaari. 2024-02-14. 1D stochastic pressure equation with log-correlated Gaussian coefficients. https://doi.org/10.1016/j.spa.2025.104808

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