Invariant measures for stochastic conservation laws on the line

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 generalizes previous work on the stochastic Burgers equation.

arXiv comment33 pages; generalized assumptions on the noise in this version

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Cited by in corpus (1)

• Jointly invariant measures for the Kardar-Parisi-Zhang Equation