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

报 告 人：王勇 副研究员

报告时间：2024年9月7日10:40-11:40

报告地点：格物楼数学研究中心528报告厅

报告摘要：In this talk, we consider 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, i.e., $\v\to 0$, in $L^{\infty}$ sense with a rate of convergence. Notably, for the limiting system \eqref{fge} obtained in the low Mach number limit, the variation of the wall temperature is allowed to be independent of the Mach number. It is also worth pointing out that the velocity field $u_{1}$ acts like a ghost since it appears at $\v$-order in the expansion, but still affects the density and temperature at $O(1)$-order. In the proof, we design a new expansion, in which the density, velocity and temperature have different expansion forms with respect to $\v$, so that the density at higher order is well defined under the Boussinesq relations and the constraint of zero average. We also introduce a new $\v$-dependent functional space, allowing us to obtain some uniform estimates on high order normal derivatives near the boundary.such uniform in $\mathfrak{c}$ estimates will be useful in the study of Newtonian limit in the future.

报告人简介：王勇，中科院数学与系统科学研究院副研究员。2012年博士毕业于中科院数学与系统科学研究院，曾获中科院数学与系统科学研究院“重要科研进展奖”、入选中科院数学与系统科学研究院“陈景润未来之星”计划，2020年获国家优秀青年科学基金资助，并主持完成面上项目1项。主要研究可压缩欧拉方程、欧拉-泊松方程、玻尔兹曼方程等方程的适定性和流体动力学极限。目前已经在Communications on Pure and Applied Mathematics, Advances in Mathematics, Archive for Rational Mechanics and Analysis和SIAM Journal on Mathematical Analysis等国际著名刊物上接受和发表学术论文30余篇。