Speaker: Huang Feimin, Researcher, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Date: Sept. 22, 2021

Time: 14：30-15：30

Location: Tencent Meeting ID: 381 986 951

Abstract:

We consider the large time behavior of strong solutions to the stochastic Burgers equation with transportation noise. It is well known that both the rarefaction wave and viscous shock wave are time-asymptotically stable for deterministic Burgers equation since the pioneer work of A. Ilin and O. Oleinik in 1964. However, the stability of these wave patterns under stochastic perturbation is not known until now. In this paper, we give a definite answer to the stability problem of the rarefaction and viscous shock waves for the 1-d stochastic Burgers equation. That is, the rarefaction wave is still stable under white noise perturbation and the viscous shock is not stable yet. Moreover, a time-convergence rate toward the rarefaction wave is obtained. To get the desired decay rate, an important inequality (denoted by Area Inequality) is derived. This inequality plays essential role in the proof, and may have applications in the related problems for both the stochastic and deterministic PDEs. This is a joint work with Dong Zhao and Su Houqi.

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