报告题目: Validity of Prandtl Expansion for Steady Compressible Navier-Stokes-Fourier Flows

报告人:   王勇 研究员(中国科学院数学与系统科学研究院)

报告摘要：

Studying steady flows is crucial in fluid dynamics for designing efficient systems (e.g., pipes, turbines, aircraft). Boundary layer study is fundamental in flying vessels surrounded by a compressible fluid, for which the classical boundary layer theory for incompressible fluid becomes inadequate. Despite its importance both from mathematical and physical standpoints, to our knowledge, there are very limited mathematical results to solve the steady compressible flows with both momentum and energy equations even for a finite Reynolds' number in the presence of mixed non-slip and in-flow boundary condition. Assume no-slip boundary conditions for the velocity field and either insulated or Dirichlet boundary conditions for the temperature field in a steady compressible fluid. In the inviscid limit $\v \rightarrow 0$ , we develop a mathematical framework for the uniform-in-$\v$ remainder estimate for the linear steady compressible Navier-Stokes-Fourier equations around a Prandtl layer profile with both velocity and thermal layers, which leads to the validity of the Prandtl layer expansion.

报告人简介： 王勇，现任中科院数学与系统科学研究院研究员，主要研究可压缩Navier-Stokes(-Poisson)方程、Euler(-Poisson)方程以及Boltzmann方程解的适定性和渐近行为。迄今发表论文40余篇，代表工作发表在CPAM、ARMA(6篇)、CMP、Adv.Math(2篇)、SIMA(11篇)、JLMS、JFA等。曾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。

报告时间: 2026.4.30(周四) 下午 2:00-3:00

报告地点: 逸夫楼1537