Global Well-Posedness and Exponential Decay for the Two-Phase Model with a Magnetic Field

IF 1.5 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2026-02-02 DOI:10.1007/s00021-025-00989-1

Xueyuan Qi

引用次数: 0

Abstract

In this paper, we study a two-phase model with a magnetic field in periodic domain \(\mathbb {T}^{N} (N=2,3)\), which was first derived by Wen and Zhu (J.Differ.Equ., 2018). By introducing a new quantity and utilizing the intrinsic structure of the system, we overcome the difficulty arising from the lack of dissipation for density of fluid and density of particles in the mixture, and establish the existence of global strong solutions in Sobolev spaces \(H^{3}\). Furthermore, we obtain the exponential decay of solutions. Our results considerably improve upon the recent works by Wen and Zhu (J.Differ.Equ., 2018) and Chen and Zhu(J.Differ.Equ., 2019).

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带磁场的两相模型的全局适定性和指数衰减

本文研究了由Wen和Zhu （j . difference . equ）首次推导的周期域中磁场为\(\mathbb {T}^{N} (N=2,3)\)的两相模型。， 2018)。通过引入一个新的量和利用系统的固有结构，克服了流体密度和混合粒子密度缺乏耗散所带来的困难，并建立了Sobolev空间\(H^{3}\)中整体强解的存在性。进一步，我们得到了解的指数衰减。我们的结果大大改进了温和朱（j.d equ）最近的工作。[j] .武汉大学学报（自然科学版），2018)。， 2019)。

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

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.