报告题目:Low Mach number Limit of Steady Thermally Driven Fluid

报告人：王勇 研究员 （中国科学院数学与系统科学研究院）

报告时间：2024年7月19日（周五）上午10:30-11:30

报告地点：理学楼A110

摘要：In this talk, we establish the existence of strong solutions to the steady non-isentropic compressible Navier-Stokes system with Dirichlet boundary conditions in bounded domains where the fluid is driven by the wall temperature, and justify its low Mach number limit in $L^{infty}$ sense with a rate of convergence. Notably, for the limiting system obtained in the low Mach number limit, the variation of the wall temperature is allowed to be independent of $varepsilon$, and it is worth pointing out that the velocity field $u_{1}$ acts like a ghost since it appears at order $v$ in the expansion and still affects $rho_{0}$ and $theta_{0}$ at $O(1)$ order. For the proof, we design a new expansion, in which the density, velocity and temperature have different expansion form with respect to the Mach number $v$, to guarantee that the density at higher $v$ order is well defined under the Boussinesq relations and the constraint of zero average. We also introduce a new $v$-dependent functional space which allows us to obtain some uniform estimates on high order normal derivatives near the boundary.

报告人介绍：王勇，中国科学院数学与系统科学研究院研究员，博士生导师，其研究工作曾获国家自然科学优秀青年基金等项目资助。主要研究兴趣为可压缩流体方程（如：Euler，Navier-Stokes及其耦合模型等）和Boltzmann方程等方程解的适定性和渐近行为。主要论文发表在Comm.Pure Appl.Math.，Arch.Ration.Mech.Anal., Adv.Math.，Comm.Math.Phys. 和SIAM J.Math.Anal.等国际著名刊物上。

邀请人：王彦霖