关于具有非齐次狄利克雷边界数据的不规则区域上纳维 - 斯托克斯方程非常弱解的适定性理论
On well-posedness theory of very weak solutions to Navier-Stokes equations on irregular domains with nonhomogeneous Dirichlet boundary data
AI总结：
本文基于相关解析理论，建立了特定有界利普希茨区域上纳维 - 斯托克斯方程非常弱解的适定性理论，该区域边界有局部绘图函数且索伯列夫乘子范数小，含利普希茨常数小的区域为特例。
AI中文摘要：
非常弱解的适定性理论是数学流体动力学的核心主题，特别是在纳维 - 斯托克斯方程的正则性理论中。它已在\(R^3\)中\(C^{2,1}\)正则性的有界区域上针对不可压缩流体流动得到充分发展。本文基于[D. Breit和A. Gaudin，ArXiv预印本：2511.19091（2025）]和[V.G. Maz'ya和T.O. Shaposhnikova，第337卷，数学科学基础教程（2009）]中的解析理论，建立了具有局部绘图函数且索伯列夫乘子范数足够小的有界利普希茨区域上纳维 - 斯托克斯方程非常弱解的适定性理论，其中包含利普希茨常数足够小的有界利普希茨区域作为特殊情况。
英文摘要：
The well-posedness theory of very weak solutions is a central topic in mathematical hydrodynamics, especially in the regularity theory for Navier-Stokes equations. It has been fully developed for incompressible fluid flows on bounded domains in R^3 of C^{2,1}-regularity. In this paper, based on the analytic theories in [D. Breit and A. Gaudin, ArXiv Preprint: 2511.19091 (2025)] and [V.G. Maz'ya and T.O. Shaposhnikova, Vol.337, Grundlehren der mathematischen Wissenschaften (2009)], we establish the well-posedness theory of very weak solutions to the Navier-Stokes equations on bounded Lipschitz domains whose boundary has local graphing functions with sufficiently small Sobolev multiplier norm, which contain the bounded Lipschitz domains with sufficiently small Lipschitz constants as a special case.
