Inviscid Burgers equation with random kick forcing in noncompact setting

Research output: Contribution to journalArticle

Abstract

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.
Original languageEnglish (US)
Article number1406.5660
JournalarXiv
StatePublished - Jun 22 2014

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Burgers Equation
Minimizer
Forcing
Hyperbolicity
Ergodic Theory
Exponential Convergence
Coalescence
Subsequence
Reverse

Keywords

  • math.PR
  • math.AP
  • math.DS
  • 37L40, 37L55, 35R60, 37H99, 60K35, 60G55

Cite this

Inviscid Burgers equation with random kick forcing in noncompact setting. / Bakhtin, Yury.

In: arXiv, 22.06.2014.

Research output: Contribution to journalArticle

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