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

Yakov G. Sinai

doi:10.1007/BF01057866

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

Yakov G. Sinai

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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 as t → ∞. If the force is the product of a periodic function of x 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 as t → ∞.

Original language	English (US)
Pages (from-to)	1-12
Number of pages	12
Journal	Journal of Statistical Physics
Volume	64
Issue number	1-2
DOIs	https://doi.org/10.1007/BF01057866
State	Published - Jul 1 1991

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/BF01057866

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AB - 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 as t → ∞. If the force is the product of a periodic function of x 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 as t → ∞.

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

Abstract

All Science Journal Classification (ASJC) codes

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