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On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions

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  • We study the low Mach number limit for the compressible Navier-Stokes system supplemented with Navier's boundary condition on an unbounded domain with compact boundary. Our main result asserts that the velocities converge pointwise to a solenoidal vector field - a weak solution of the incompressible Navier-Stokes system - while the fluid density becomes constant. The proof is based on a variant of local energy decay property for the underlying acoustic equation established by Kato.
    Mathematics Subject Classification: Primary: 35Qxx; Secondary: 35D30, 76Nxx.


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