Journal of Statistical Physics

, Volume 64, Issue 1–2, pp 1–12 | Cite as

Two results concerning asymptotic behavior of solutions of the Burgers equation with force

  • Ya. G. Sinai
Articles

Abstract

We consider the Burgers equation with an external force. For the case of the force periodic in space and time we prove the existence of a solution periodic in space and time which is the limit of a wide class of solutions ast → ∞. If the force is the product of a periodic function ofx and white noise in time, we prove the existence of an invariant distribution concentrated on the space of space-periodic functions which is the limit of a wide class of distributions ast → ∞.

Key words

Burgers equation white noise local central limit theorem partition function 

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References

  1. 1.
    E. Hopf,Commun. Pure Appl. Math. 3:201 (1950).Google Scholar
  2. 2.
    J. M. Burgers,The Nonlinear Diffusion Equation (Reidel, Dordrecht, 1974).Google Scholar
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    B. Simon,Functional Integration and Quantum Physics (Academic Press, New York, 1979).Google Scholar
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    B. V. Gnedenko and A. N. Kolmogorov,Limit Theorems for Sums of Independent Random Variables (FizMatGiz, Moscow, 1949).Google Scholar

Copyright information

© Plenum Publishing Corporation 1991

Authors and Affiliations

  • Ya. G. Sinai
    • 1
    • 2
  1. 1.Landau Institute of Theoretical PhysicsMoscowUSSR
  2. 2.Princeton UniversityPrinceton

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