Mathematics – Analysis of PDEs
Scientific paper
2004-02-27
Mathematics
Analysis of PDEs
35 pages, no figure
Scientific paper
10.1007/s00220-004-1254-9
Both experimental and numerical studies of fluid motion indicate that initially localized regions of vorticity tend to evolve into isolated vortices and that these vortices then serve as organizing centers for the flow. In this paper we prove that in two dimensions localized regions of vorticity do evolve toward a vortex. More precisely we prove that any solution of the two-dimensional Navier-Stokes equation whose initial vorticity distribution is integrable converges to an explicit self-similar solution called ``Oseen's vortex''. This implies that the Oseen vortices are dynamically stable for all values of the circulation Reynolds number, and our approach also shows that these vortices are the only solutions of the two-dimensional Navier-Stokes equation with a Dirac mass as initial vorticity. Finally, under slightly stronger assumptions on the vorticity distribution, we also give precise estimates on the rate of convergence toward the vortex.
Gallay Thierry
Wayne Eugene C.
No associations
LandOfFree
Global stability of vortex solutions of the two-dimensional Navier-Stokes equation 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 Global stability of vortex solutions of the two-dimensional Navier-Stokes equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Global stability of vortex solutions of the two-dimensional Navier-Stokes equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-294460