The resolvent problem of the linearized compressible Navier-Stokes equation around a given constant state is considered in an infinite layer [formula omitted], under the no slip boundary condition for the momentum. It is proved that the linearized operator is sectorial in [formula omitted]for [formula omitted]. The Lpestimates for the resolvent are established for all [formula omitted]. The estimates for the high frequency part of the resolvent are also derived, which lead to the exponential decay of the corresponding part of the semigroup.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology