Incompletely Parabolic Problems in Fluid Dynamics

Source 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. In this paper we analyze such systems; in particular we treat the mixed initial-boundary value problem. In many applications there is a small parameter $\varepsilon$ multiplying the coefficient for the highest derivative. The energy method is used to derive well-posed boundary conditions such that, when $\varepsilon$ tends to zero, the reduced problem is also well posed.