Large Time Behavior of Strong Solutions for Stochastic Burgers Equation with Transport Noise
发布时间：2021年09月20日
浏览次数：4911
发布者: He Liu
主讲人： Houqi Su (AMSS-CAS)
活动时间： 从 2021-10-13 15:15 到 17:00
场地： 北京国际数学研究中心，全斋全29教室
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. Ilin and O. Oleinik [31] in 1964. However, the stability of these wave patterns under stochastic perturbation is not known until now. In this talk, 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 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.
