发表机构
School of Mathematics, Shandong University（山东大学数学学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究水平周期带中稳态不可压缩Navier-Stokes流的存在性与粘性消失极限，以Poiseuille流为基准构造对称近似解，证明在相容性条件下存在对称解并以最优速率收敛。
AI 中文摘要
我们研究在水平周期带中，具有无滑移边界条件和关于中线对称的外力作用下，稳态不可压缩Navier-Stokes流的存在性及粘性消失极限。以Poiseuille流作为零阶Euler剖面，我们构造了高阶对称近似解，并建立了相应非线性误差方程对称解的存在性。在外力满足适当的相容性条件下，该构造产生一族关于中线对称的稳态Navier-Stokes解，且该族解以最优速率收敛到给定的Poiseuille流。
英文摘要
We study the existence and vanishing viscosity limit of steady incompressible Navier-Stokes flows in a horizontally periodic strip with no slip boundary conditions and midline symmetric forcing. Taking a Poiseuille flow as the leading order Euler profile, we construct higher order symmetric approximate solutions and establish the existence of a symmetric solution to the associated nonlinear error equation. Under suitable compatibility conditions on the forcing, this construction yields a family of midline symmetric steady Navier-Stokes solutions that converges to the prescribed Poiseuille flow at the optimal rate.
