分数阶各向异性 Navier-Stokes 方程初值问题解的唯一性
Uniqueness of Solutions to Initial Value Problems of Fractional Anisotropic Navier-Stokes Equations
DOI: 10.12677/PM.2021.1112218, PDF, HTML,    国家自然科学基金支持
作者: 刘敉秀, 孙小春*：西北师范大学数学与统计学院，甘肃 兰州
关键词: 分数阶各向异性 Navier-Stokes 方程；Sobolev 空间；乘积公式；Fractional Anisotropic Navier-Stokes Equations； Sobolev Space； Product Formula
摘要: 该文证明了仅有水平分数阶耗散的不可压缩 Navier-Stokes 方程初值问题在各向异性 Sobolev 函数空间 H2α−2,s( ℝ3) 中解的唯一性，其中1/2 < α ≤ 1, α/2 < s < 2α −α/2。 证明的关键是给出 (α,s,t)满足适当范围的函数乘积公式，进而利用 Fourier 分析技巧得出结论。
Abstract: In this paper, we proved the uniqueness of the solution of the initial value problem of incompressible Navier-Stokes equation with only horizontal fractional dissipation in the anisotropic Sobolev function space H2α−2,s( ℝ3), where 1/2 < α ≤ 1, α/2 < s < 2α −α/2. The key of the proof is to give the product formula of the function when (α, s, t) satisfies the appropriate range, and then the conclusion is obtained by using Fourier analysis technique.
文章引用：刘敉秀, 孙小春. 分数阶各向异性 Navier-Stokes 方程初值问题解的唯一性[J]. 理论数学, 2021, 11(12): 1957-1966. https://doi.org/10.12677/PM.2021.1112218

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