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arXiv · 2201.12641

Invariant measures for stochastic conservation laws on the line

Theodore D. Drivas·Alexander Dunlap·Cole Graham·Joonhyun La·Lenya Ryzhik
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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.

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Theodore D. Drivas, Alexander Dunlap, Cole Graham, Joonhyun La, Lenya Ryzhik. 2022-01-29. Invariant measures for stochastic conservation laws on the line. https://doi.org/10.1088/1361-6544/acdb3a

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