中科院数学与系统科学研究院
数学研究所
学术报告
偏微分方程研讨班
报告人：Fei Wang (Shanghai JiaoTong Univerisity)
题 目：Global Existence of Weak Solutions for Compressible Navier--Stokes--Fourier Equations with the Truncated Virial Pressure Law in Recent progress on mathematical theory of boundary layer
时 间：2023.07.21（星期五）09:30-10:30
地 点：思源楼S803
摘 要：This paper concerns the existence of global weak solutions {\it \`a la Leray} for compressible Navier--Stokes--Fourier system with periodic boundary conditions and the truncated virial pressure law which is assumed to be thermodynamically unstable. More precisely, the main novelty is that the pressure law is not assumed to be monotone with respect to the density. This provides the first global weak solutions result for the compressible Navier-Stokes-Fourier system with such kind of pressure law which is strongly used as a generalization of the perfect gas law. The paper is based on a new construction of approximate solutions through an iterative scheme and fixed point procedure which could be very helpful to design efficient numerical schemes. Note that our method involves the recent paper by the authors published in Nonlinearity (2021) for the compactness of the density when the temperature is given.
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题 目：On the Euler+Prandtl expansion for the Navier-Stokes equations
时 间：2023.07.21（星期五）10:30-11:30
地 点：思源楼S803
摘 要：We establish the validity of the Euler+Prandtl approximation for solutions of the Navier-Stokes equations in the half plane with Dirichlet boundary conditions, in the vanishing viscosity limit, for initial data which are analytic only near the boundary, and Sobolev smooth away from the boundary. Our proof does not require higher order correctors, and works directly by estimating an L 1 -type norm for the vorticity of the error term in the expansion Navier-Stokes−(Euler+Prandtl). An important ingredient in the proof is the propagation of local analyticity for the Euler equation, a result of independent interest.
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