Sharp condition of global existence for nonlinear Schrödinger equation with a harmonic potential

Threshold for Blowup and Stability for Nonlinear Schrödinger Equation with Rotation

“…see [37] for related discussions. The analogue of Theorem 6.6 was studied in [33] when Ω = 0, V = |x| 2 . For further investigation we refer to [41] for the treatment on the minimal mass problem in the case of the inhomogeneous NLS.…”

Finite dimensional global attractor for a damped fractional anisotropic Schrödinger type equation with harmonic potential

“…On the contrary, to the best of our knowledge, the literature for fractional Schrödinger equations is still expending and rather young. If α = 2, (1.3) becomes the standard Gross-Pitaevskii equation which has been extensively studied as a fundamental equation in modern mathematical physics specially for Bose-Einstein condensates (see [10,4,34] for instance). In the special case when V = 0 we refer the reader; for well-posedness results and existence of traveling waves for the resulting conservative fractional NLS; to [5,25,26,21,13,45,7] and the references therein.…”

Finite dimensional global attractor for a Bose-Einstein equation in a two dimensional unbounded domain

“…He also has established a lower bound of the blow up time under classical conditions on n and σ (see [7] and the references therein). In [16], the author has derived out a sharp sufficient condition (related to the mass of the ground state solution) for the global existence either in the critical case (σ = 2 n ) or with supercritical nonlinearities (i.e: σ ∈] 2 n , 2 n−2 [ if n ≥ 3 and σ ∈] 2 n , +∞[ if n = 1, 2). We complete this introduction with some definitions.…”