Asymptotic behavior of the semigroup associated with the linearized compressible Navier-Stokes equation in an infinite layer (Q2475483)

The author considers the linearisation of the Navier-Stokes equations in a steady state posed in an infinite layer \(\mathbb R^m\times (0,a)\). Using the author's previous result that this generates an analytic semigroup [Funkc. Ekvacioj, Ser. Int. 50, No. 2, 287--337 (2007; Zbl 1180.35413)], \(L^p\)-decay properties are established for all \(1\leq p \leq \infty\). In contrast to the mixed hyperbolic-parabolic behaviour for the problem posed in the whole space [\textit{D. Hoff} and \textit{K. Zumbrun}, Z. Angew. Math. Phys. 48, No. 4, 597--614 (1997; Zbl 0882.76074)], it is shown that the leading order part of the semigroup for large times is an \(m\)-dimensional heat semigroup.