1D stochastic pressure equation with log-correlated Gaussian coefficients

Type: Preprint

Publication Date: 2024-02-14

Citations: 0

DOI: https://doi.org/10.48550/arxiv.2402.09127

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.

Locations

  • arXiv (Cornell University) - View - PDF

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