报告题目：Steady Prandtl Expansion for Subsonic Flows
报告人：王勇研究员（中科院数学与系统科学研究院）
时间：10月24日15:00-16：00
地点：数学学院211
摘要：Assuming construction of Prandtl and its high order corrections for compressible fluids with small Mach number, we establish nonlinear remainder bound and justify the validity of the Prandtl layer expansion in the inviscid limit for an insulated boundary. To solve the full steady compressible Navier-Stokes system, which consists a div-curl reduction of the momentum equations to an elliptic system for the stream function $\phi $ as well as an transport equation for the pressure $p$. The contruction of $\phi $ is based on an improved Guo-Iyer's $H^{4}$ theory for incompressible flows via development of a $H_{00}^{1/2}$ technique with a type viscous-inflow BC,
and the pressure $p$ is solved by imposing a key additional \textit{viscous-inflow} boundary condition. We reformulate the ]energy equation in terms of the pseudo entropy $S$ (not the temperature), which exhibits a crucial uniform bound for the final closure.
报告人简介：王勇研究员2012年博士毕业于中科院数学与系统科学研究院，现任中科院数学与系统科学研究院研究员。主要研究非线性双曲守恒律、可压缩Navier-Stokes方程、Boltzmann方程等方程的适定性和流体动力学极限。公开发表SCI论文20余篇，主要论文发表在CPAM、 Adv. Math.、Arch. Ration. Mech. Anal.和 SIAM J. Math. Anal.、等国际著名刊物上。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、入选中科院青年创新促进会。目前主持国家自然科学基金面上项目一项，2020年获国家优秀青年科学基金资助。
