Large time behavior of solutions to the compressible Navier-Stokes equation around a given constant state is considered in an infinite layer Rn-1 ×(0,a)n ≥ 2, under the no slip boundary condition for the velocity. The Lp decay estimates of the solution are established for all 1≤ p≤∞. It is also shown that the time-asymptotic leading part of the solution is given by a function satisfying the n - 1 dimensional heat equation. The proof is given by combining a weighted energy method with time-weight functions and the decay estimates for the associated linearized semigroup.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Geometry and Topology