6 papers
Compactly Supported Strong Ill-Posedness of the Two-Dimensional Euler Flow in
Yingzhe Ban, Maotuo Guo, Qi Zhang
We prove strong ill-posedness for the two-dimensional incompressible Euler equation in the endpoint velocity space . Given any compactly supported smooth di…
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(\…
Magnetic norm inflation at the Besov endpoint for viscous non-resistive incompressible MHD
Yingzhe Ban, Boling Guo, Maotuo Guo
We prove magnetic-field norm inflation at the origin for the viscous, non-resistive incompressible magnetohydrodynamic equations on , , in the endpoint space \[ \dot B…
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…
A compensated Piola principle for critical nondiffusive parabolic systems
Maotuo Guo
We introduce a compensated Piola graph method for Lagrangian stability estimates in critical homogeneous Besov spaces below the usual product threshold. For , $2d\le p<\inft…
Moving One-Component Regularity Criteria for the 3D Incompressible MHD Equations
Maotuo Guo
We establish a scaling-critical continuation criterion for the three-dimensional incompressible magnetohydrodynamic equations in with arbitrary positive viscosity an…