Masahiro Suzuki (Nagoya Institute of Technology)
Title:
Stationary flows for viscous heat-conductive fluid in a perturbed half-space
Abstract:
In this talk, we consider the non-isentropic compressible Navier--Stokes equation in a perturbed half-space with an outflow boundary condition as well as the supersonic condition. This equation models a compressible viscous, heat-conductive, and Newtonian polytropic fluid. We show the unique existence of stationary solutions for the perturbed half-space. The stationary solution depends on all directions and has multidirectional flow. We also prove the asymptotic stability of this stationary solution.
Tatsuki Yamamoto (Waseda University)
Title:
Nonhomogeneous boundary value problem for the steady Navier-Stokes equations in multiply-connected domains
Abstract:
We consider the nonhomogeneous boundary value problem for the steady Navier-Stokes equations under the slip boundary conditions in a two-dimensional bounded domain with multiple boundary components. By the incompressibility condition of the fluid, the total flux of the given boundary datum through the boundary must be zero. We prove that this problem has a solution if the friction coefficient is sufficiently large compared with the kinematic viscosity constant and the curvature of the boundary. No additional assumption (other than the necessary requirement of zero total flux through the boundary) is imposed on the boundary datum. This talk is based on the joint work with Prof. Giovanni P. Galdi (University of Pittsburgh).
Tong Yang (Wuhan University)
Title:
Some recent study on viscous fluid with strong boundary layers
Abstract:
It is a classical problem in fluid dynamics about the stability and instability of different fluid patterns in various physical settings, especially in the high Reynolds number limit with no-slip boundary condition. In this talk, we will first review the background and some recent main progress on Prandtl boundary layer theory. Then we will discuss a recent work on the structural stability of the steady 3D Prandtl system. We will also discuss effect of bulk viscosity on the Tollmien-Schlichting waves and the high Reynolds number limit for the steady 2D compressible flow.