Work

A Critical one-component regularity criteria for the three-dimensional Navier--Stokes equations

Year: 2026

Type: preprint

Abstract: We establish two critical one-component regularity criteria for the three-dimensional incompressible Navier--Stokes equations. First, for divergence-free initial data $u_0\in H^1(\mathbb R^3)$, we prove that a strong solution can be continued beyond a finite time $T$ provided that \[ u^3\in L^2\bigl(0,T;\dot B^{3/2}_{2,r}(\mathbb R^3)\bigr) \qquad\text{for some }2

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.34637

Authors: Maotuo, Guo, Shiyang, Xiong, Chuankai, Zhao

Institutions: Harbin University of Science and Technology, Shanghai Jiao Tong University, Beijing University of Technology

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W7214788963

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