Open Access
2016 Inviscid Burgers equation with random kick forcing in noncompact setting
Yuri Bakhtin
Electron. J. Probab. 21: 1-50 (2016). DOI: 10.1214/16-EJP4413


We develop ergodic theory of the inviscid Burgers equation with random kick forcing in noncompact setting. The results are parallel to those in our recent work on the Burgers equation with Poissonian forcing. However, the analysis based on the study of one-sided minimizers of the relevant action is different. In contrast with previous work, finite time coalescence of the minimizers does not hold, and hyperbolicity (exponential convergence of minimizers in reverse time) is not known. In order to establish a One Force — One Solution principle on each ergodic component, we use an extremely soft method to prove a weakened hyperbolicity property and to construct Busemann functions along appropriate subsequences.


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Yuri Bakhtin. "Inviscid Burgers equation with random kick forcing in noncompact setting." Electron. J. Probab. 21 1 - 50, 2016.


Received: 7 July 2015; Accepted: 12 May 2016; Published: 2016
First available in Project Euclid: 19 May 2016

zbMATH: 1338.37117
MathSciNet: MR3508684
Digital Object Identifier: 10.1214/16-EJP4413

Primary: 35R60 , 37H99 , 37L40 , 37L55 , 60G55 , 60K35

Keywords: Burgers equation , Busemann functions , invariant distributions , Last passage percolation , One Force – One Solution Principle , SPDE

Vol.21 • 2016
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