The Motion of a Rigid Body in a Viscous Fluid: Results for Strong Solutions, Uniqueness and Integrability Properties

IF 1.5 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-10-27 DOI:10.1007/s00021-025-00977-5

Paolo Maremonti, Filippo Palma

引用次数: 0

Abstract

In this note, we show two results in the setting of Galdi-Silvestre strong solutions for the rigid body-viscous fluid interaction. The former, under an additional integrability assumption on the gradient of the initial datum, proves that the time derivative of the solution belongs to \(L^2(0,T;L^2(\Omega ))\). The latter, thanks to a further assumption only on one solution, proves that the uniqueness holds in the quoted setting. However, our extra assumption for the uniqueness is certainly verified under the integrability assumption on the gradient of the initial datum. Hence, the set of solutions enjoying the uniqueness is not empty.

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粘性流体中刚体的运动：强解的结果，唯一性和可积性

在本文中，我们给出了刚体-粘性流体相互作用的Galdi-Silvestre强解的两个结果。前者在初始基准梯度的附加可积假设下，证明了解的时间导数属于\(L^2(0,T;L^2(\Omega ))\)。后者，由于只对一个解作进一步的假设，证明唯一性在引用的设置中成立。然而，在初始基准的梯度上的可积性假设下，我们对唯一性的额外假设得到了验证。因此，具有唯一性的解集不是空的。

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.