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<p>In this paper, we investigate the existence of a unique global smooth solution to the three-dimensional incompressible Navier-Stokes equations and provide a concise proof. We establish a new global well-posedness result that allows the initial data to be arbitrarily large within the critical space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\dot{B}_{\infty,\infty}^{-1}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <msubsup> <mrow> <mover> <mi>B</mi> <mo>˙</mo> </mover> </mrow> <mrow> <mi mathvariant="normal">∞</mi> <mo>,</mo> <mi mathvariant="normal">∞</mi> </mrow> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> </math></EquationSource> </InlineEquation>, while still satisfying the nonlinear smallness condition.</p>

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Global Smooth Solutions to Navier-Stokes Equations with Large Initial Data in Critical Space

  • 期刊论文

  • 发表日期：

    2026年1月29日

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  • Hai-na Li,
  • Yi-ran Xu

摘要

In this paper, we investigate the existence of a unique global smooth solution to the three-dimensional incompressible Navier-Stokes equations and provide a concise proof. We establish a new global well-posedness result that allows the initial data to be arbitrarily large within the critical space \(\dot{B}_{\infty,\infty}^{-1}\) B ˙ ∞ , ∞ − 1 , while still satisfying the nonlinear smallness condition.