On a Lp-estimate for the linearized compressible Navier–Stokes equations with the Dirichlet boundary conditions

In this paper a special Lp-estimate for the linearized compressible Navier–Stokes in the Lagrangian coordinates for the Dirichlet boundary conditions is obtained. The constant in the estimate does not depend on the length of time interval [0,T]. The result is essential to obtain an existence for regular solutions for the nonlinear problem with the lowest class of regularity in Lp-spaces