The Burgers equation with Poisson random forcing

Abstract

We consider the Burgers equation on the real line with forcing given by Poissonian noise with no periodicity assumption. Under a weak concentration condition on the driving random force, we prove existence and uniqueness of a global solution in a certain class. We describe its basin of attraction that can also be viewed as the main ergodic component for the model. We establish existence and uniqueness of global minimizers associated to the variational principle underlying the dynamics. We also prove the diffusive behavior of the global minimizers on the universal cover in the periodic forcing case.

Published in at http://dx.doi.org/10.1214/12-AOP747 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (1)

• Burgers Turbulence

Cited by in corpus (6)

• On global solutions of the random Hamilton-Jacobi equations and the KPZ problem
• Busemann functions and Gibbs measures in directed polymer models on ${\mathbb{Z}}^2$
• The stationary horizon and semi-infinite geodesics in the directed landscape
• Zero temperature limit for directed polymers and inviscid limit for stationary solutions of stochastic Burgers equation
• Jointly invariant measures for the Kardar-Parisi-Zhang Equation
• Simultaneous global inviscid Burgers flows with periodic Poisson forcing