178 citations · 185 across the 6 of their papers we have counts for
7 papers
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…
Solitary Wave Dynamics in an External Potential
J. Frohlich, S. Gustafson, B. L. G. Jonsson +1
We study the behavior of solitary-wave solutions of some generalized nonlinear Schrödinger equations with an external potential. The equations have the feature that in the absence…
Asymptotic Stability and Completeness in the Energy Space for Nonlinear Schrödinger Equations with Small Solitary Waves
Stephen Gustafson, Kenji Nakanishi, Tai-Peng Tsai
In this paper we study a class of nonlinear Schrödinger equations which admit families of small solitary wave solutions. We consider solutions which are small in the energy space $…