92 research outputs found
Motion of a vortex sheet on a sphere with pole vortices
We cons i der the motion of a vortex sheet on the surface of a unit sphere in the presence of point vortices xed on north and south poles.Analytic and numerical research revealed that a vortex sheet in two-dimensional space has the following three properties.First,the vortex sheet is linearly unstable due to Kelvin-Helmholtz instability.Second,the curvature of the vortex sheet diverges in nite time.Last,the vortex sheet evolves into a rolling-up doubly branched spiral,when the equation of motion is regularized by the vortex method.The purpose of this article is to investigate how the curvature of the sphere and the presence of the pole vortices
Proceedings of the 35th Sapporo Symposium on Partial Differential Equations
conf: The 35th Sapporo Symposium on Partial Differential Equations (Room 203, Faculty of Science Building #5, Hokkaido University , August 23-25, 2010
Proceedings of minisemester on evolution of interfaces, Sapporo 2010
conf: Special Project A, Proceedings of minisemester on evolution of interfaces, Sapporo (Department of Mathematics, Hokkaido University, July 12- August 13, 2010
The geometry of a vorticity model equation
We provide rigorous evidence of the fact that the modified
Constantin-Lax-Majda equation modeling vortex and quasi-geostrophic dynamics
describes the geodesic flow on the subgroup of orientation-preserving
diffeomorphisms fixing one point, with respect to right-invariant metric
induced by the homogeneous Sobolev norm and show the local existence
of the geodesics in the extended group of diffeomorphisms of Sobolev class
with .Comment: 24 page
On the analyticity and Gevrey class regularity up to the boundary for the Euler Equations
We consider the Euler equations in a three-dimensional Gevrey-class bounded
domain. Using Lagrangian coordinates we obtain the Gevrey-class persistence of
the solution, up to the boundary, with an explicit estimate on the rate of
decay of the Gevrey-class regularity radius
- …