Artículos de revistas
Incompressible Flow Around A Small Obstacle And The Vanishing Viscosity Limit
Registro en:
Communications In Mathematical Physics. , v. 287, n. 1, p. 99 - 115, 2009.
103616
10.1007/s00220-008-0621-3
2-s2.0-60449107501
Autor
Iftimie D.
Lopes Filho M.C.
Nussenzveig Lopes H.J.
Institución
Resumen
In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior domain converge to solutions of the Euler system in the full space when both viscosity and the size of the obstacle vanish. We prove that this convergence is true assuming two hypotheses: first, that the initial exterior domain velocity converges strongly in L 2 to the full-space initial velocity and second, that the diameter of the obstacle is smaller than a suitable constant times viscosity, or, in other words, that the obstacle is sufficiently small. The convergence holds as long as the solution to the limit problem is known to exist and stays sufficiently smooth. 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