Stability of rarefaction wave for stochastic Burgers equation

时间:2020.10.29 16:50-18:20

地点:腾讯会议 251 824 105



现就职于中国科学院应用数学研究所,任中科院华罗庚首席研究员。曾获得美国工业与应用数学协会杰出论文奖(The SIAM Outstanding Paper Prize),国家杰出青年科学基金,国家自然科学二等奖。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一系列突出成果。已在Comm. Math. Phys., Arch. Ration. Mech. Anal., Adv. Math. 等学术期刊发表论文数十篇。


The large time behavior of strong solutions to the stochastic Burgers equation is considered in this paper. It is first shown that the unique global strong solution to the one dimensional stochastic Burgers equation time-asymptotically tend to a rarefaction wave, that is, the rarefaction wave is non-linearly stable under white noise perturbation for stochastic Burgers equation. A time-convergence rate is also obtained. Moreover, an important inequality (denoted by Area Inequality) is derived. This inequality plays essential role in the estimates, and may have applications in the related problems, in particular for the time-decay rate of solutions of both the stochastic and deterministic PDEs. As an application, the stability of planar rarefaction wave is shown stable for a two dimensional viscous conservation law with stochastic force.