Stability of noncharacteristic boundary-layers for the compressible nonisentropic Navier-Stokes equations.

摘要

In this dissertation, we prove the stability of noncharacteristic viscous boundary layers for the compressible nonisentropic Navier-Stokes equations subject to no-slip suction-type boundary conditions.;These boundary conditions correspond to the situation of an airfoil with microscopic holes through which gas is pumped from the surrounding flow, the microscopic suction imposing a fixed normal velocity while the macroscopic suface imposes standard temperature conditions as in flow past a (nonporous) plate. This configuration was suggested by Prandtl and tested experimentally by G. I. Taylor as a means to reduce drag by stablizing laminar flow. It was implemented in the NASA F-16XL experimental aircraft program in the 1990's with reported 25% reduction in drag at supersonic speeds.;In [8], existence and stability of noncharacterisitic viscous boundary layers for the compressible Navier-Stokes equations has been proved for pure Dirichlet and pure Neumann boundary conditions.;In this dissertation, our boundary conditions are mixed Dirichlet-Neumann and we establish stability in this case.