Asymptotic limit of the Gross-Pitaevskii equation with general initial data

Fu Cai Li; Chi Kun Lin; Kung Chien Wu

doi:10.1007/s11425-015-5104-3

Asymptotic limit of the Gross-Pitaevskii equation with general initial data

Fu Cai Li^*
, Chi Kun Lin
, Kung Chien Wu

^*Corresponding author for this work

Department of Financial and Actuarial Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

This paper mainly concerns the mathematical justification of the asymptotic limit of the Gross-Pitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.

Original language	English
Pages (from-to)	1113-1126
Number of pages	14
Journal	Science China Mathematics
Volume	59
Issue number	6
DOIs	https://doi.org/10.1007/s11425-015-5104-3
Publication status	Published - 1 Jun 2016

Keywords

Gross-Pitaevskii equation
asymptotic limit
general initial data
incompressible Euler equation

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10.1007/s11425-015-5104-3

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title = "Asymptotic limit of the Gross-Pitaevskii equation with general initial data",

abstract = "This paper mainly concerns the mathematical justification of the asymptotic limit of the Gross-Pitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.",

keywords = "Gross-Pitaevskii equation, asymptotic limit, general initial data, incompressible Euler equation",

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N2 - This paper mainly concerns the mathematical justification of the asymptotic limit of the Gross-Pitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.

AB - This paper mainly concerns the mathematical justification of the asymptotic limit of the Gross-Pitaevskii equation with general initial data in the natural energy space over the whole space. We give a rigorous proof of the convergence of the velocity fields defined through the solutions of the Gross-Pitaevskii equation to the strong solution of the incompressible Euler equations. Furthermore, we also obtain the rates of the convergence.

KW - Gross-Pitaevskii equation

KW - asymptotic limit

KW - general initial data

KW - incompressible Euler equation

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Asymptotic limit of the Gross-Pitaevskii equation with general initial data

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Keywords

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