ŠT—vFThis talk is concerned with the stability of stationary solutions
of the incompressible Navier-Stokes equation and the corresponding
artifical compressible system. The latter system is obtained by adding
the time derivative of the pressure with a small parameter to the
continuity equation. Both systems have the same sets of stationary
solutions and the incompressible system is obtained from the artificial
compressible one in the zero small parameter limit which is a singular
limit. It is shown that if a stationary solution is stable as a solution
of the incompressible Navier-Stokes equation and satisfies some
smallness condition, then the stationary solution is also stable as a
solution of the artificial compressible system. This talk is based on a
joint work with Prof. Takaaki Nishida (Kyoto Univ.) and Ms. Yuka
Teramoto (Kyushu Univ.).