INCOMPLETELY PARABOLIC PROBLEMS IN FLUID DYNAMICS.

Abstract

Some partial differential equations encountered in physical applications are of incompletely parabolic type; the Navier-Stokes equations in fluid dynamics are a typical example. Such systems are analyzed in this paper. In particular, the mixed initial-boundary value problem is treated. In many applications there is a small parameter epsilon multiplying the coefficient for the highest derivative. The energy method is used to derive well-posed boundary conditions such that, when epsilon tends to zero, the reduced problem is also well posed.