On a Stokes System Arising in a Free Surface Viscous Flow of a Horizontally Periodic Fluid with Fractional Boundary Operators

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2024-02-12 DOI:10.1007/s00021-023-00850-3

Daisuke Hirata

引用次数: 0

Abstract

In this note we investigate the initial-boundary value problem for a Stokes system arising in a free surface viscous flow of a horizontally periodic fluid with fractional boundary operators. We derive an integral representation of solutions by making use of the multiple Fourier series. Moreover, we demonstrate a unique solvability in the framework of the Sobolev space of \(L^2\)-type.

查看原文本刊更多论文

关于水平周期流体自由表面粘性流动中出现的斯托克斯系统与分数边界算子

摘要在本论文中，我们研究了在水平周期流体的自由表面粘性流动中出现的斯托克斯系统的初始边界值问题，该系统带有分数边界算子。我们利用多重傅里叶级数推导出解的积分表示。此外，我们还证明了在\(L^2\) 型 Sobolev 空间框架下的唯一可解性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

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.