腾讯会议ID：851 159 533
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.
简介:黄飞敏，博士生导师，中国科学院数学与系统科学研究院华罗庚首席研究员，国家杰出青年基金获得者。2015年入选国家万人计划，2013年获国家自然科学奖二等奖，2004年获美国工业与应用数学协会杰出论文奖。主要从事非线性偏微分方程的研究工作，在非线性双曲守恒律、可压缩Navier-Stokes方程、Boltzmann方程等重要领域取得了一系列突出成果。已在Adv. Math.，Arch. Ration. Mech. Anal.，Comm. Math. Phys.，Comm. Partial Differential Equations.和SIAM J. Math. Anal.等国际著名刊物发表论文数十篇。