178 citations · 185 across the 6 of their papers we have counts for
5 papers · 1 filter
Scattering for the Gross-Pitaevskii equation
S. Gustafson, K. Nakanishi, T. -P. Tsai
We investigate the asymptotic behavior at time infinity of solutions close to a non-zero constant equilibrium for the Gross-Pitaevskii (or Ginzburg-Landau Schroedinger) equation. W…
Regularity criteria for suitable weak solutions of the Navier-Stokes equations near the boundary
Stephen Gustafson, Kyungkeun Kang, Tai-Peng Tsai
We present some new regularity criteria for ``suitable weak solutions'' of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions a…
Schrodinger Flow Near Harmonic Maps
S. Gustafson, K. Kang, T. -P. Tsai
For the Schrödinger flow from to the 2-sphere , it is not known if finite energy solutions can blow up in finite time. We study equivariant solutions whose en…
Effective Dynamics of Magnetic Vortices
S. Gustafson, I. M. Sigal
We study solutions of Ginzburg-Landau-type evolution equations (both dissipative and Hamiltonian) with initial data representing collections of widely-spaced vortices. We show that…
The Stability of Magnetic Vortices
S. Gustafson, I. M. Sigal
We study the linearized stability of n-vortex solutions of the magnetic Ginzburg-Landau (or Abelian-Higgs) equations. We prove that the fundamental vortices (n=1,-1) are stable for…