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Erschienen in:
2011 | OriginalPaper | Buchkapitel
The Compressible Navier–Stokes System
verfasst von : Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
Erschienen in: Fourier Analysis and Nonlinear Partial Differential Equations
Verlag: Springer Berlin Heidelberg
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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.