Low Mach number limit on thin domains

We consider the compressible Navier-Stokes system describing the motion of a viscous fluid confined to a straight layer $Ω_δ=(0,δ)\times\mathbb{R}^2$. We show that the weak solutions in the 3D domain converge strongly to the solution of the 2D incompressible Navier-Stokes equations (Euler equations) when the Mach number $ε$ tends to zero as well as $δ\rightarrow 0$ (and the viscosity goes to zero).

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