Partial Regularity of Navier-Stokes Equations
Lihe Wang
TL;DR
This paper establishes that solutions to the Navier-Stokes equations are regular except on a set of Hausdorff dimension 1, using a geometric approach, a new compactness lemma, and harmonic function properties.
Contribution
It introduces a novel geometric method and a new compactness lemma to analyze the partial regularity of Navier-Stokes solutions.
Findings
Solutions are regular outside a set of Hausdorff dimension 1
New compactness lemma developed for the analysis
Utilizes monotonicity of harmonic functions in the proof
Abstract
We prove, with a more geometric approach, that the solutions to the Navier-Stokes equations are regular up to a set of Hausdorff dimension 1. The main tool for the proof is a new compactness lemma and the monotonicity property of harmonic functions.
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Taxonomy
TopicsStability and Controllability of Differential Equations · Navier-Stokes equation solutions · Advanced Mathematical Modeling in Engineering