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临界阻尼型Navier-Stokes方程在Lei-Lin-Gevrey空间 X a,σ 0 ( ？ 3 )中的局部适定性
The Local Suitability of the Critical Damping Navier-Stokes Equation in Lei-Lin-Gevrey Space X a,σ 0 ( ？ 3 )

DOI: 10.12677/pm.2025.152055, PP. 138-146

Keywords: 阻尼，Navier-Stokes方程，Lei-Lin-Gevrey空间，局部解
Damping, Navier-Stokes Equations, Lei-Lin-Gevrey Space, Local Solution

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Abstract:

本文证明带有临界型阻尼项的Navier-Stokes方程在Lei-Lin-Gevrey空间 X a,σ 0 ( ？ 3 ) 中存在唯一的局部解。文章利用不动点定理和热方程解的有关性质来证明这一主要结论。
In this paper, it is proved that the Navier-Stokes equation with critical damping terms has a unique local solution in the Lei-Lin-Gevrey space X a,σ 0 ( ？ 3 ) . In this paper, the main conclusion is proved by using the fixed point theorem and the related properties of the solution of the heat equation.

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