皮塔耶夫斯基超流模型的小数据全局存在解

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-04-17 DOI:10.1088/1361-6544/ad3cae

Juhi Jang, Pranava Chaitanya Jayanti and Igor Kukavica

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引用次数: 0

摘要

我们研究了皮塔耶夫斯基（1959 Sov. Phys. JETP8 282-7）推导的超流体微尺度模型，以描述氦-4的超流体和正常流体相之间的相互作用动力学。该模型涉及非线性薛定谔方程（NLS）和纳维-斯托克斯方程，通过双向非线性弛豫机制相互耦合。根据 NLS 中非线性的性质，我们证明了该系统的全局/近似全局解的存在性--波函数和速度强，密度弱。

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Small-data global existence of solutions for the Pitaevskii model of superfluidity

We investigate a micro-scale model of superfluidity derived by Pitaevskii (1959 Sov. Phys. JETP8 282–7) to describe the interacting dynamics between the superfluid and normal fluid phases of Helium-4. The model involves the nonlinear Schrödinger equation (NLS) and the Navier–Stokes equations, coupled to each other via a bidirectional nonlinear relaxation mechanism. Depending on the nature of the nonlinearity in the NLS, we prove global/almost global existence of solutions to this system in —strong in wavefunction and velocity, and weak in density.

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来源期刊

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.