Navier's slip and incompressible limits in domains with variable bottoms
Eduard Feireisl Josef Málek Antonín Novotný
We consider unsteady flows of compressible Navier-Stokes-Fourier equations in domains with bottoms that are not flat and where the fluid fulfils Navier's slip boundary conditions. Dealing with weak solutions whose long-time and large data existence has been recently established, we investigate their behavior for vanishing Mach number (the square of this small parameter appears also in the Navier slip condition), and prove their convergence towards the weak solution of the so-called Boussinesq approximation with the no-slip boundary condition. The fact that we treat the Navier boundary condition brings several interesting features in the analysis of acoustic waves, in particular the strong convergence of the velocity field.
keywords: Compressible Navier-Stokes-Fourier system weak solution Oberbeck-Boussinesq approximation Navier's slip boundary conditions low Mach number limit singular limit.
On incompressible limits for the Navier-Stokes system on unbounded domains under slip boundary conditions
Donatella Donatelli Eduard Feireisl Antonín Novotný
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.
keywords: singular limits compressible fluids low Mach number unbounded domains. Navier-Stokes equations

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