一类加权函数空间中的Navier-Stokes Cauchy问题

IF 1.2 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-02-20 DOI:10.1007/s00021-025-00923-5

Paolo Maremonti, Vittorio Pane

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引用次数: 0

摘要

我们考虑了加权勒贝格空间中具有初始基准的Navier-Stokes Cauchy问题。重量是一个径向函数，在无穷远处增加。我们的研究部分遵循了Galdi和Maremonti的论文（J Math Fluid Mech 25:7, 2023）。引用论文的作者考虑了一个关于稳定流体运动稳定性的特殊研究。该结果适用于3D和小数据。这里，相对于静态的扰动，我们推广了结果。我们研究nD Navier-Stokes Cauchy问题，\(n\ge 3\)。证明了一个唯一正则解的存在性（局部）。此外，该解具有空间渐近衰减，其衰减阶数与权值有关。

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The Navier–Stokes Cauchy Problem in a Class of Weighted Function Spaces

We consider the Navier–Stokes Cauchy problem with an initial datum in a weighted Lebesgue space. The weight is a radial function increasing at infinity. Our study partially follows the ideas of the paper by Galdi and Maremonti (J Math Fluid Mech 25:7, 2023). The authors of the quoted paper consider a special study of stability of steady fluid motions. The results hold in 3D and for small data. Here, relatively to the perturbations of the rest state, we generalize the result. We study the nD Navier–Stokes Cauchy problem, \(n\ge 3\). We prove the existence (local) of a unique regular solution. Moreover, the solution enjoys a spatial asymptotic decay whose order of decay is connected to the weight.

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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.