Jointly stationary solutions of periodic Burgers flow

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

v2, 33 pages

References in corpus (2)

• Global structure of semi-infinite geodesics and competition interfaces in Brownian last-passage percolation
• Viscous shock solutions to the stochastic Burgers equation

Cited by in corpus (1)

• Simultaneous global inviscid Burgers flows with periodic Poisson forcing