On the Nonhomogeneous Navier--Stokes System with Navier Friction Boundary Conditions

We address the issue of existence of weak solutions for the nonhomogeneous Navier--Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the convergence, as the viscosity goes to zero, of weak solutions f...

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Bibliographic Details
Published in:SIAM journal on mathematical analysis 2013-01, Vol.45 (4), p.2576-2595
Main Authors: Ferreira, Lucas C. F., Planas, Gabriela, Villamizar-Roa, Elder J.
Format: Article
Language:English
Subjects:
Boundary conditions
Convergence
Density
Euler equations
Fluid flow
Friction
Mathematical analysis
Navier-Stokes equations
Viscosity
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Summary:We address the issue of existence of weak solutions for the nonhomogeneous Navier--Stokes system with Navier friction boundary conditions allowing the presence of vacuum zones and assuming rough conditions on the data. We also study the convergence, as the viscosity goes to zero, of weak solutions for the nonhomogeneous Navier--Stokes system with Navier friction boundary conditions to the strong solution of the Euler equations with variable density, provided that the initial data converge in $L^{2}$ to a smooth enough limit. [PUBLICATION ABSTRACT]
ISSN:0036-1410
1095-7154
DOI:10.1137/12089380X