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Workshop on Partial Differential Equation

题目： Large time behavior of strong solutions for stochastic Burgers equation

报告人：黄飞敏 研究员 （中科院）

时间：2021年11月3日下午2：30-3：30

地点：腾讯会议  会议ID：441 349 834

摘要:  We consider the large time behavior of strong solutions to the stochastic Burgers equation with transport 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. M. Ilin and O. A. 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 with transport noise. That is, the rarefaction wave is still stable under transport 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. The talk is based on a joint work with Zhao Dong and Houqi Su.

联系人： 牛冬娟

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