PDE系列报告

报告题目： Asymptotic stability of planar rarefaction wave  under periodic perturbation for 3-d Navier-Stokes equations

报告人：黄飞敏 教授

报告时间：2022年4月20日 周三15:00-16:00

腾讯会议：861-157-051

摘要： In this talk, we study a Cauchy problem for the 3-d compressible isentropic Navier-Stokes equations, in which the initial data is a 3-d periodic perturbation around a planar rarefaction wave. We prove that the solution of the Cauchy problem exists

globally and tends to the background rarefaction wave in the $ L^\infty(\R^3) $ space as $ t\to +\infty. $

The result reveals that even though the initial perturbation has infinite oscillations at the far field and is not integrable

along any direction of space, the planar rarefaction wave is nonlinearly stable for the 3-d N-S

equations. The key point is to construct a suitable ansatz $ (\rhot, \uvt) $ to carry the same oscillations as those of the

solution $ (\rho, \uv) $ at the far field in the normal direction of the rarefaction wave, so that the

difference $ (\rho-\rhot, \uv-\uvt) $ belongs to some Sobolev space and the energy method is available.

报告人简介：黄飞敏，中科院华罗庚首席研究员。 曾获2013年国家自然科学奖二等奖（第一完成人），国家杰出青年基金获得者，万人计划领军人才，获2004年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一系列突出成果，广受国内外同行的关注。在“Adv. Math.”、“Arch. Ration. Mech. Anal.”、“Comm. Math. Phys.”、“ Ann. PDE”、“Comm. PDE”、“SIAM J. Math. Anal.”等国际著名刊物发表论文100多篇。

黄飞敏