Planar stationary solution to initial boundary value problem for compressible heat conducting gas in R^3_+
报告题目(Title)： Planar stationary solution to initial boundary value problem for compressible heat conducting gas in R^3_+
报告人(Speaker)：王腾 副教授 北京工业大学
地点(Place)：腾讯会议 ID：592 629 086
时间(Time)：2021-07-1（星期四）， 2:00-3:00 pm （Beijing Time）
邀请人(Inviter)：许孝精, 袁迪凡
报告摘要
In this talk, we are concerned with the large-time behavior of planar stationary solution to the compressible heat conducting gas in three dimensions under outflow or inflow condition. (1) It is shown that a corresponding planar stationary solution to outflow problem is time-asymptotically stable, provided the initial perturbation in a certain Sobolev space and the boundary strength are sufficiently small. (2) Moreover, the convergence rate of the solution toward the stationary solution is obtained, provided that the initial perturbation belongs to the weighted Sobolev space. (3) We prove the time-asymptotic stability of planar stationary solution to inflow problem in subsonic case and transonic case provided the initial perturbation in a certain Sobolev space and the boundary strength are sufficiently small. Each proof is given by deriving a-priori estimates of the perturbation from the stationary wave by using a time and space weighted energy method.
主讲人简介
王腾，博士，副教授、校聘教授、硕士生导师。入选北京工业大学“高端人才队伍建设计划—优秀人才”。主要从事非线性偏微分方程的研究工作，研究兴趣为流体力学方程组和动力学方程的相关数学理论，主要包括流体力学方程组解的极限行为、动力学方程以及流体—粒子耦合模型解的大时间行为等。2014年至今共计发表SCI论文20篇，主要成果发表在国际重要刊物“Arch. Rational Mech. Anal.”、“Indiana Univ. Math. J.”、“SIAM J. Math. Anal.”、“Nonlinearity”、“J. Differential Equations”、“J. Math. Fluid Mech.”等。
