An Energy Method for the Equations of Motion of Compressible Viscous and Heat-Conductive Fluids

摘要

A priori estimates for solutions of the quasilinear hyperbolic-parabolic equations governing the initial value problem describing the motion of compressible, viscous and heat-conductive, Newtonian fluids are derived by means of a new energy method. This technique enables us to simplify and unify our previous results on the global existence in time and uniqueness of smooth solutions of these equations for sufficiently smooth and 'small' initial data and to obtain their rate of decay. (Author)