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<p>In this work, the local decomposition of pressure in the Navier-Stokes equations is dynamically refined to prove that a relevant critical energy of a Leray-type solution inside a backward paraboloid—regardless of its aperture—is controlled near the vertex by a critical behavior confined to a neighborhood of the paraboloid’s boundary. This neighborhood excludes the interior near the vertex and remains separated from the temporal profile of the vertex, except at the vertex itself. Moreover, we present a refined scaling-invariant regularity result.</p>

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Dynamic Refinement of Pressure Decomposition in Navier-Stokes Equations

  • 期刊论文

  • 发表日期：

    2025年9月3日

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  • Pedro Gabriel Fernández-Dalgo

摘要

In this work, the local decomposition of pressure in the Navier-Stokes equations is dynamically refined to prove that a relevant critical energy of a Leray-type solution inside a backward paraboloid—regardless of its aperture—is controlled near the vertex by a critical behavior confined to a neighborhood of the paraboloid’s boundary. This neighborhood excludes the interior near the vertex and remains separated from the temporal profile of the vertex, except at the vertex itself. Moreover, we present a refined scaling-invariant regularity result.