三维各向异性纳维-斯托克斯系统的全局小解析解

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

Archive for Rational Mechanics and Analysis Pub Date : 2024-10-30 DOI:10.1007/s00205-024-02051-2

Ning Liu, Ping Zhang

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引用次数: 0

摘要

本文证明了三维各向异性纳维-斯托克斯（Navier-Stokes）系统的全局解析解的存在性，其初始数据很小，且在垂直变量中解析。我们还将证明，在 \(t>0 后不久，该解在水平变量中也将是解析的。\此外，我们还将证明解在水平变量中的解析半径\(R_\textrm{h}(t),\)与\(\sqrt{t}\)之间的比值满足\(\lim _{t\rightarrow 0_+}\frac{R_\textrm{h}(t)}{sqrt{t}}=\infty .\)

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Global Small Analytic Solution of 3-D Anisotropic Navier-Stokes System

In this paper, we prove the global existence of analytic solution for 3D anisotropic Navier-Stokes system with initial data which is small and analytic in the vertical variable. We shall also prove that this solution will be analytic in the horizontal variables soon after \(t>0.\) Furthermore, we show that the ratio between the analytic radius, \(R_\textrm{h}(t),\) of the solution in the horizontal variables and \( \sqrt{t}\) satisfies \(\lim _{t\rightarrow 0_+}\frac{R_\textrm{h}(t)}{\sqrt{t}}=\infty .\)

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来源期刊

Archive for Rational Mechanics and Analysis 物理-力学

CiteScore

5.10

自引率

8.00%

发文量

审稿时长

4-8 weeks

期刊介绍： The Archive for Rational Mechanics and Analysis nourishes the discipline of mechanics as a deductive, mathematical science in the classical tradition and promotes analysis, particularly in the context of application. Its purpose is to give rapid and full publication to research of exceptional moment, depth and permanence.