On a \(L_{p}\)-estimate for the linearized compressible Navier-Stokes equations with the Dirichlet boundary conditions. (Q1867228)

The authors consider an initial-boundary value problem for linearized compressible Navier-Stokes equations in Lagrangian coordinates and with Dirichlet boundary conditions. Using energy estimates, standard imbedding theorems and Marcinkiewicz-Mikhlin theorems on \(L_p\)-multipliers, the authors derive for the solution a special \(L_p\)-estimate with a constant independent of the length of time interval \([0; T]\).