Resolvent estimates for the linearized operator in Lp associated with motion of compressible viscous fluids

We consider the resolvent problem for the linearized system of equations that describe motion of compressible viscous barotropic fluids in a bounded domain with the Navier boundary condition. This problem has uniquely a solution in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{W}^{1}_{p} \times (W^{2}_{p})^{n}}$$\end{document} satisfying Lp estimates for any 1 < p < ∞. Moreover, resolvent estimates for the linearized operator of the above system in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{W}^{1}_{p} \times (L_{p})^{n}}$$\end{document} are established. Our main results yield clearly that the linearized operator is the infinitesimal generator of a uniformly bounded analytic semigroup on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\dot{W}^{1}_{p} \times (L_{p})^{n}}$$\end{document}.