Global smooth solutions to Navier-Stokes equations with large initial data in critical space

Haina Li; Yiran Xu

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arXiv · 2502.20059

Global smooth solutions to Navier-Stokes equations with large initial data in critical space

Haina Li·Yiran Xu

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Abstract

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 $\dot{B}^{-1}_{\infty,\infty}$, while still satisfying the nonlinear smallness condition.

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Haina Li, Yiran Xu. 2025-02-27. Global smooth solutions to Navier-Stokes equations with large initial data in critical space. https://arxiv.org/abs/2502.20059

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