临界阻尼型Navier-Stokes方程在Lei-Lin-Gevrey空间      X       a,σ   0    (            ℝ     3          )中的局部适定性

doi:10.12677/pm.2025.152055

期刊菜单

临界阻尼型Navier-Stokes方程在Lei-Lin-Gevrey空间 $X_{a, σ}^{0} (ℝ^{3})$ 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} (ℝ^{3})

DOI: 10.12677/pm.2025.152055, PDF,
作者: 刘爱博, 常莹：辽宁师范大学数学学院，辽宁大连
关键词: 阻尼；Navier-Stokes方程；Lei-Lin-Gevrey空间；局部解；Damping； Navier-Stokes Equations； Lei-Lin-Gevrey Space； Local Solution

摘要: 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} (ℝ^{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。

Abstract: 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} (ℝ^{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.

文章引用：刘爱博, 常莹. 临界阻尼型Navier-Stokes方程在Lei-Lin-Gevrey空间

X_{a, σ}^{0} (ℝ^{3})

中的局部适定性[J]. 理论数学, 2025, 15(2): 138-146. https://doi.org/10.12677/pm.2025.152055

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