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<p>Using a more geometric approach, we demonstrate that the solutions to the Navier–Stokes equations remain regular except on a set with a null Hausdorff measure of dimension 1. The proof primarily relies on a new compactness lemma and the monotonicity property of harmonic functions. The combination of linear and nonlinear approximation schemes makes the proof clear and transparent.</p>

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Partial Regularity for Navier-Stokes Equations

  • 期刊论文

  • 发表日期：

    2025年3月6日

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  • Lihe Wang

摘要

Using a more geometric approach, we demonstrate that the solutions to the Navier–Stokes equations remain regular except on a set with a null Hausdorff measure of dimension 1. The proof primarily relies on a new compactness lemma and the monotonicity property of harmonic functions. The combination of linear and nonlinear approximation schemes makes the proof clear and transparent.