偏微分方程研讨班

中科院数学与系统科学研究院

数学研究所

偏微分方程研讨班

时  间：2022.11.21（星期一）

地  点：腾讯会议：931-169-269，会议密码：1121

n  上午9 :00-10 :00

报告人：张映辉 教授 （广西师范大学）

题  目：Stability and instability of a generic non--conservative compressible two--fluid model

摘 要：We are concerned with stability and instability of the steady state (1,0,1,0) for a generic non–conservative compressible two–fluid model in R³. Under the assumption that the initial fraction densities are close to the constant state (1,1) in H³and the initial velocities are small in H² with s[0,1], it is shown that  is the critical value of s on the stability of the model in question. More precisely, when 0s<, the steady state (1,0, 1,0) is nonlinearly globally stable; and conversely, the steady state (1,0,1,0) is nonlinearly unstable in the sense of Hadamard when <s1. Furthermore, for the critical case s= if the initial data satisfy additional regularity assumption, then the steady state (1,0,1,0) is nonlinearly globally stable.

n  上午10 :00- 11 :00

报告人：琚强昌 研究员

（北京应用物理与计算数学研究所）

题 目：Diffusion limit of the compressible Euler-P1 approximation model arising from radiation hydrodynamics

摘 要：We first show the nonequilibrium-diffusion limit of the compressible Euler-P1 approximation model arising in radiation hydrodynamics as the Mach number tends to zero when the initial data is well-prepared. In particular, the effect of the large temperature variation upon the limit is taken into account. The model leads to a singular problem which fails to fall into the category of the classical theory of singular limits for quasilinear hyperbolic equations. By introducing an appropriate normed space of solutions and exploiting the structure of the system, we establish the uniform local existence of smooth solutions and the convergence of the model to the incompressible nonhomogeneous Euler system coupled with a diffusion equation. Moreover, we also prove the nonequilibrium-diffusion limit of the compressible Euler-P1 approximation model when the Mach number is fixed.