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The mathematical theory of low Mach number flows. (English) Zbl 1094.35094
In this paper one can find a very interesting approach to the mathematical theory of the passage from compressible to incompressible fluid flows as the Mach number tends to zero. Starting from a system of equations which allows to treat simultaneously the three most commonly studied models: the isentropic incompressible Euler equations, the non-isentropic compressible Euler equations, and the barotropic compressible Navier-Stokes equations, the author considers an appropriate scaling which leads to the determination of a small parameter related with the Mach number, and so to obtain a system of equations in which the small parameter appears explicitly. Using a multiple-scale expansion the system solution is analyzed and proved that to be convergent, in the sense of certain Sobolev norm, to the appropriate limit profile as the Mach number tends to zero. Further extensions to related situations and open problems are presented.

MSC:
35Q30 Navier-Stokes equations
76G25 General aerodynamics and subsonic flows
35Q35 PDEs in connection with fluid mechanics
35C20 Asymptotic expansions of solutions to PDEs
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