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Uniform regularity for the incompressible Navier-Stokes system with variable density and Navier boundary conditions. (English) Zbl 1427.35214

The authors study the vanishing viscosity limit of the incompressible Navier-Stokes equations with variable density in the three-dimensional half-space. By showing the uniform regularity for strong solution, and establishing the uniform estimate in conormal Sobolev spaces, the author prove the \(L^\infty\) convergence of the strong solution to that of the Euler equations, which improved the known \(L^2\) convergence.
Reviewer: Cheng He (Beijing)

MSC:

35Q35 PDEs in connection with fluid mechanics
35B65 Smoothness and regularity of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
35D35 Strong solutions to PDEs
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids

Citations:

Zbl 1274.35266
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References:

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