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.
    • Motion of a vortex sheet on a sphere with pole vortices.
  • 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.
  • Motion of unstable polygonal ring of vortex points (N-ring) on sphere with pole vortices.
• Mathematical models for fluid equations
  • Blow-up solutions for the Constantine-Lax-Majda equation with a generalized viscosity term
  • On global solutions for the Constantine-Lax-Majda equation with a generalized viscosity term
• Chaotic Advection
  • Topological Chaos embedded in the blinking vortex system.