2025/04/25 by Benjamin Fehrman, Fehrman, Benjamin · 2 citations
Economics, Econometrics and Finance · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2504.18370
openalex publication_date 2025/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The results of the author and Gess [27] develop a robust well-posedness theory for a broad class of conservative stochastic PDEs, with both probabilistically stationary and non-stationary Stratonovich noise, and with irregular noise coefficients like the square root. However, one case left untreated by [27] is the case of SPDEs that combine conservative, non-stationary Stratonovich noise with square root-like nonlinearities. Such equations arise naturally in the fluctuating hydrodynamics of inhomogenous systems, and a new analysis is required to handle certain discontinuous coefficients appearing in their Itô formulations. We treat the discontinuities by showing that the equation exhibits a novel regularization of the logarithm of the solution, and establish the well-posedness by building on the concept of a stochastic kinetic solution introduced in [27].