Research Works
Vortex sheet problems
Evolution of vortex sheets
The motion of a 2-D vortex sheet in a background shear flow.
Complex interactions of two vortex sheets.
A fast summation method and long time mixing evolution of 2-D vortex sheet.
Numerical computation of a three-dimensional vortex sheet in a swirl flow.
Singularity formation
Singularity formation of the vortex sheet on a sphere.
Analytic continuation of the Birkhoff-Rott equation to a rolling up spiral in complex time domain.
Formation of curvature singularity along vortex line in an axi-symmetric, swirling flow.
Motions of Point vortices
The motion of three point vortices on a sphere.
Mathematical models for fluid equations
Blow-up and global solutions for the Constantine-Lax-Majda equation with a generalized viscosity term
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