Incompressible flow around a small obstacle and the vanishing viscosity limit

Details Incompressible flow around a small obstacle and the vanishing viscosity limit Incompressible flow around a small obstacle and the vanishing viscosity limit

2008-01-31

arxiv.org/abs/0801.4935v1

Comm. Math. Phys. 287 (2009), 99-115

Mathematics

Analysis of PDEs

Submitted for publication

Scientific paper

10.1007/s00220-008-0621-3

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 hypothesis: 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. This work complements the study of incompressible flow around small obstacles, which has been carried out in [1,2,3] [1] D. Iftimie and J. Kelliher, {\it Remarks on the vanishing obstacle limit for a 3D viscous incompressible fluid.} Preprint available at http://math.univ-lyon1.fr/~iftimie/ARTICLES/viscoushrink3d.pdf . [2] D. Iftimie, M. C. Lopes Filho, and H. J. Nussenzveig Lopes. {\it Two dimensional incompressible ideal flow around a small obstacle.} Comm. Partial Differential Equations {\bf 28} (2003), no. 1-2, 349--379. [3] D. Iftimie, M. C. Lopes Filho, and H. J. Nussenzveig Lopes. {\it Two dimensional incompressible viscous flow around a small obstacle.} Math. Ann. {\bf 336} (2006), no. 2, 449--489.

Affiliated with

Also associated with

No associations

Rating

Incompressible flow around a small obstacle and the vanishing viscosity limit does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Incompressible flow around a small obstacle and the vanishing viscosity limit, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Incompressible flow around a small obstacle and the vanishing viscosity limit will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-204838