On an estimate for the linearized compressible Navier--Stokes equations in the \(L_p\)-framework (Q2717688)

The author considers a system of PDEs which can be arrived at by a linearization of the compressible Navier--Stokes equations. Under the assumption that the solution has a compact support in space, the author gives \(L^p\) estimates of the solution over the time-space cylinder, \(p\geq 2\), with a constant independent of time. NEWLINENEWLINENEWLINEThis result can be applied to construct a global-in-time solution for the compressible Navier--Stokes equations with sharp regularity. NEWLINENEWLINENEWLINEThe main tool here is the Marcinkiewicz (sometimes also called the Lizorkin) multiplier theorem.