The Compressible Navier–Stokes System
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In Chapter 10 we present a more complicated system of partial differential equations coming from fluid mechanics, the so-called barotropic compressible Navier–Stokes equations. Those equations are of mixed hyperbolic-parabolic type. We show how we may take advantage of the results of Chapter 3 and the techniques introduced in Chapter 2 so as to obtain local (or global) unique solutions with critical regularity. The last part of this chapter is dedicated to the study of the low Mach number limit for this system. It is shown that under appropriate assumptions on the data, the limit solution satisfies the incompressible Navier–Stokes system studied in Chapter 5.
KeywordsStokes Equation Global Existence Strong Solution Besov Space Local Theory
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