Global well-posedness of a system from quantum hydrodynamics for small data

Q4 Mathematics

Confluentes Mathematici Pub Date : 2015-01-01 DOI:10.5802/cml.21

C. Audiard

引用次数: 1

Abstract

This article describes a joint work of the author with B.Haspot on the existence and uniqueness of global solutions for the Euler-Korteweg equations in the special case of quantum hydrodynamics. Our aim here is to sketch how one can construct global small solutions of the Gross-Pitaevskii equation and use the so-called Madelung transform to convert these into solutions without vacuum of the quantum hydrodynamics. A key point is to bound the the solution of the Gross-Pitaevskii equation away from 0, this condition is fullfilled thanks to recent scattering results.

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小数据下量子流体力学系统的全局适定性

本文描述了作者与B.Haspot在量子流体力学特殊情况下关于Euler-Korteweg方程整体解的存在唯一性的联合工作。本文的目的是描述如何构造Gross-Pitaevskii方程的全局小解，并利用所谓的马德隆变换将其转化为量子流体力学的无真空解。关键是要使Gross-Pitaevskii方程的解远离0，由于最近的散射结果，这个条件得到了满足。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.