4 papers
A Critical one-component regularity criteria for the three-dimensional Navier--Stokes equations
Guo Maotuo, Xiong Shiyang, Zhao Chuankai
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(\…
A Critical Chemin--Lerner Regularity Criterion via One Velocity Component for the Three-Dimensional Navier--Stokes Equations
Maotuo Guo, Wendong Wang, Shiyang Xiong
We prove a scaling-critical regularity criterion involving only one velocity component for finite-energy suitable weak solutions of the three-dimensional incompressible Navier--Sto…
Positive-regularity norm inflation for the 3D hypodissipative Navier--Stokes equations
Guirong Tang, Shiyang Xiong
We prove same-space norm inflation for the three-dimensional hypodissipative Navier--Stokes equations with dissipation , . Let and \[ 0<s<1-2α+\frac3…
On the Regularity of Navier-Stokes Equations in Critical Space
Shiyang Xiong, Liqun Zhang
This paper focuses on the regularity of the Navier-Stokes equations in critical space. Let and denote suitable weak solution of the Navier-Stokes equations in…