Global well posedness for the Gross–Pitaevskii equation with an angular momentum rotational term

In this paper, we establish the global well posedness of the Cauchy problem for the Gross–Pitaevskii equation with a rotational angular momentum term in the space ℝ2. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  J Dalibard,et al.  Stationary states of a rotating Bose-Einstein condensate: routes to vortex nucleation. , 2001, Physical review letters.

[2]  T. Cazenave Semilinear Schrodinger Equations , 2003 .

[3]  E. Gross Structure of a quantized vortex in boson systems , 1961 .

[4]  B. Simon,et al.  Schrödinger operators with magnetic fields , 1981 .

[5]  W. Ketterle,et al.  Bose-Einstein condensation , 1997 .

[6]  Yanzhi Zhang,et al.  Dynamics of the center of mass in rotating Bose--Einstein condensates , 2007 .

[7]  Qiang Du,et al.  Dynamics of Rotating Bose-Einstein Condensates and its Efficient and Accurate Numerical Computation , 2006, SIAM J. Appl. Math..

[8]  T. Tao,et al.  Endpoint Strichartz estimates , 1998 .

[9]  J. R. Ensher,et al.  Dynamics of component separation in a binary mixture of Bose-Einstein condensates , 1998 .

[10]  Rémi Carles,et al.  Semi-classical Schrödinger equations with harmonic potential and nonlinear perturbation , 2003, math/0702656.

[11]  Dalibard,et al.  Vortex formation in a stirred bose-einstein condensate , 1999, Physical review letters.

[12]  E. M. Lifshitz,et al.  Quantum mechanics: Non-relativistic theory, , 1959 .

[13]  C. E. Wieman,et al.  Vortices in a Bose Einstein condensate , 1999, QELS 2000.

[14]  Weizhu Bao,et al.  Ground, Symmetric and Central Vortex States in Rotating Bose-Einstein Condensates , 2005 .

[15]  B. Simon,et al.  Schrödinger operators with magnetic fields. I. general interactions , 1978 .

[16]  Transverse Evolution Operator for the Gross-Pitaevskii Equation in Semiclassical Approximation , 2005, math-ph/0511081.