Sharp Threshold of the Gross-Pitaevskii Equation with Trapped Dipolar Quantum Gases

Li Ma, Jing Wang

Type: Article

Publication Date: 2011-08-28

Citations: 15

DOI: https://doi.org/10.4153/cmb-2011-181-2

Abstract

Abstract In this paper, we consider the Gross-Pitaevskii equation for the trapped dipolar quantum gases. We obtain the sharp criterion for the global existence and finite time blow-up in the unstable regime by constructing a variational problem and the so-called invariant manifold of the evolution flow.

Locations

Canadian Mathematical Bulletin - View - PDF

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+	Strong Instability of Standing Waves for the Nonlinear Schrödinger Equation in Trapped Dipolar Quantum Gases	2020	Binhua Feng Qingxuan Wang
+	Cross-invariant manifolds for the Gross–Pitaevskii–Poisson equation	2022	X. K. Zhou Shihui Zhu
+ PDF Chat	Finite time blow-up for the nonlinear Schrödinger equation in trapped dipolar quantum gases with arbitrarily positive initial energy	2020	Yi Yuan Binhua Feng
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Works Cited by This (7)

Action	Title	Year	Authors
+	Singular Integrals and Differentiability Properties of Functions.	1971	Elias M. Stein
+	The threshold for the focusing Gross–Pitaevskii equation with trapped dipolar quantum gases	2011	Li Ma Pei Cao
+ PDF Chat	Sharp thresholds of blow-up and global existence for the coupled nonlinear Schrödinger system	2008	Li Ma Lin Zhao
+	Nonlinear Schr�dinger equations and sharp interpolation estimates	1983	Michael I. Weinstein
+	Sharp conditions of global existence for nonlinear Schrödinger and Klein–Gordon equations	2002	Jian Zhang
+ PDF Chat	Dipolar Bose-Einstein condensates with dipole-dependent scattering length	2006	Shai Ronen Daniele C. E. Bortolotti D. Blume John L. Bohn
+ PDF Chat	Trapped atomic condensates with anisotropic interactions	2000	S. Yi Li You