## The compressible Euler equations in a bounded domain: Existence of solutions and the incompressible limit.(English)Zbl 0612.76082

The author considers the Euler equations for nonisentropic compressible inviscid fluids in a bounded domain. The description of the fluid is completed by the equation of state $$\rho =f(P/\lambda^ 2,S)$$ where $$\rho$$ is the density, P the pressure, S the entropy and the parameter $$\lambda$$ is essentially the inverse of the Mach number. First the author proves the local (in time) existence of a classical solution for any fixed $$\lambda$$. Afterwards he shows that the solutions converge, as $$\lambda \to +\infty$$, to the corresponding solution of the equations for incompressible inviscid fluids with variable density.
Reviewer: P.Secchi

### MSC:

 76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics 35Q30 Navier-Stokes equations
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### References:

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