Invariant measures for stochastic conservation laws on the line
- 20 July 2023
- journal article
- research article
- Published by IOP Publishing in Nonlinearity
- Vol. 36 (9) , 4553-4584
Abstract
We consider a stochastic conservation law on the line with solution-dependent diffusivity, a super-linear, sub-quadratic Hamiltonian, and smooth, spatially-homogeneous kick-type random forcing. We show that this Markov process admits a unique ergodic spatially-homogeneous invariant measure for each mean in a non-explicit unbounded set. This generalises previous work on the stochastic Burgers equation.Keywords
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Funding Information
- Division of Mathematical Sciences (DMS-1910023)
- Office of Naval Research (N00014-17-1-2145)
- Institute for Advanced Study (Charles Simonyi Endowment)
This publication has 18 references indexed in Scilit:
- Zero Temperature Limit for Directed Polymers and Inviscid Limit for Stationary Solutions of Stochastic Burgers EquationJournal of Statistical Physics, 2018
- On global solutions of the random Hamilton–Jacobi equations and the KPZ problemNonlinearity, 2018
- Inviscid Burgers equation with random kick forcing in noncompact settingElectronic Journal of Probability, 2016
- Multidimensional Potential Burgers TurbulenceCommunications in Mathematical Physics, 2015
- Turbulence for the generalised Burgers equationRussian Mathematical Surveys, 2014
- Invariant measure of scalar first-order conservation laws with stochastic forcingProbability Theory and Related Fields, 2014
- Sharp Estimates for Turbulence in White-Forced Generalised Burgers EquationGeometric and Functional Analysis, 2013
- Space-time stationary solutions for the Burgers equationJournal of the American Mathematical Society, 2013
- Large-Time Behavior for Viscous and Nonviscous Hamilton--Jacobi Equations Forced by Additive NoiseSIAM Journal on Mathematical Analysis, 2005
- Groups of automorphisms of Borel spacesTransactions of the American Mathematical Society, 1963