Jointly stationary solutions of periodic Burgers flow
Probability
2025-03-11 v2 Mathematical Physics
math.MP
Abstract
For the one dimensional Burgers equation with a random and periodic forcing, it is well-known that there exists a family of invariant measures, each corresponding to a different average velocity. In this paper, we consider the coupled invariant measures and study how they change as the velocity parameter varies. We show that the derivative of the invariant measure with respect to the velocity parameter exists, and it can be interpreted as the steady state of a diffusion advected by the Burgers flow
Keywords
Cite
@article{arxiv.2310.11647,
title = {Jointly stationary solutions of periodic Burgers flow},
author = {Alexander Dunlap and Yu Gu},
journal= {arXiv preprint arXiv:2310.11647},
year = {2025}
}
Comments
v2, 33 pages