Dynamics of Solutions to the Gross-Pitaevskii Equation Describing Dipolar Bose-Einstein Condensates

被引：1

作者：

Bellazzini, Jacopo ^{[1
]}

Forcella, Luigi ^{[2
,3
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, Pisa, Italy

[2] Heriot Watt Univ, Dept Math, Edinburgh, Scotland

[3] Maxwell Inst Math Sci, Dept Math, Edinburgh, Scotland

来源：

QUALITATIVE PROPERTIES OF DISPERSIVE PDES | 2022年 / 52卷

基金：

英国工程与自然科学研究理事会;

关键词：

NONLINEAR SCHRODINGER-EQUATION; GLOBAL WELL-POSEDNESS; BLOW-UP; CAUCHY-PROBLEM; QUANTUM GASES; SCATTERING; THRESHOLD; NLS;

D O I：

10.1007/978-981-19-6434-3_2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We review some recent results on the long-time dynamics of solutions to the Gross-Pitaevskii equation (GPE) governing non-trapped dipolar quantum gases. We describe the asymptotic behaviors of solutions for different initial configurations of the initial datum in the energy space, specifically for data below, above, and at the mass-energy threshold. We revisit some properties of powers of the Riesz transforms by means of the decay properties of the integral kernel associated to the parabolic biharmonic equation. These decay properties play a fundamental role in establishing the dynamical features of the solutions to the studied GPE.

引用

页码：25 / 57

页数：33

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