Asymptotic Behavior of the Linearized Semigroup at Space-Periodic Stationary Solution of the Compressible Navier-Stokes Equation

摘要

The asymptotic behavior of the linearized semigroup at spatially periodic stationary solution of the compressible Navier-Stokes equation in a periodic layer of R-n (n = 2,3) is investigated. It is shown that if the Reynolds and Mach numbers are sufficiently small, then the linearized semigroup is decomposed into two parts; one behaves like a solution of an n - 1 dimensional linear heat equation as time goes to infinity and the other one decays exponentially.