2014/11/14 by Benjamin Gess, Panagiotis E. Souganidis, Gess, Benjamin +1 · 8 citations
Economics, Econometrics and Finance · Engineering · Mathematics · #Applied mathematics #Combinatorics #Computer science #Conservation law #Entropy (arrow of time) #Geometry #Homogeneous #Invariant (physics) #Invariant measure #Mathematical analysis #Mathematical physics #Mathematics #Navier-Stokes equation solutions #Physics #Regularization (linguistics) #Scalar (mathematics) #Stability and Controllability of Differential Equations #Statistical physics #Stochastic processes and financial applications #math.AP #math.PR #msc:35L65 #msc:35R60 #msc:H6015
paper · pdf · doi:10.1002/cpa.21646
published in Communications on Pure and Applied Mathematics 70(8), 1562-1597 (Wiley) · 28 pages
arxiv created 2016/03/29 · arxiv updated 2016/03/30 · openalex publication_date 2016/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Abstract We study the long‐time behavior and regularity of the pathwise entropy solutions to stochastic scalar conservation laws with random‐in‐time spatially homogeneous fluxes and periodic initial data. We prove that the solutions converge to their spatial average, which is the unique invariant measure of the associated random dynamical system, and provide a rate of convergence, the latter being new even in the deterministic case for dimensions higher than 2. The main tool is a new regularization result in the spirit of averaging lemmata for scalar conservation laws, which, in particular, implies a regularization by noise‐type result for pathwise quasi‐solutions.© 2016 Wiley Periodicals, Inc.