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arXiv · 2006.10049

Ergodicity of Burgers' system

Szymon Peszat·Krystyna Twardowska·Jerzy Zabczyk
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Abstract

We consider a stochastic version of a system of coupled two equations formulated by Burgers with the aim to describe the laminar and turbulent motions of a fluid in a channel. The existence and uniqueness of the solution as well as the irreducibility property of such system were given by Twardowska and Zabczyk. In the paper the existence of a unique invariant measure is investigated. The paper generalizes the results of Da Prato, Debussche and Temam, and Da Prato and Gatarek, dealing with one equation describing the turbulent motion only.

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Szymon Peszat, Krystyna Twardowska, Jerzy Zabczyk. 2020-06-17. Ergodicity of Burgers' system. https://arxiv.org/abs/2006.10049

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