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Remarks on the Blowup Criteria for Oldroyd Models
Zhen Lei, Nader Masmoudi, Yi Zhou
We provide a new method to prove and improve the Chemin-Masmoudi criterion for viscoelastic systems of Oldroyd type in \cite{CM} in two space dimensions. Our method is much easier…
Global Regularity of the 3D Axi-symmetric Navier-Stokes Equations with Anisotropic Data
Thomas Y. Hou, Zhen Lei, Congming Li
In this paper, we study the 3D axi-symmetric Navier-Stokes Equations with swirl. We prove the global regularity of the 3D Navier-Stokes equations for a family of large anisotropic…
A Complete Global Solution to the Pressure Gradient Equation
Zhen Lei, Yuxi Zheng
We study the domain of existence of a solution to a Riemann problem for the pressure gradient equation in two space dimensions. The Riemann problem is the expansion of a quadrant o…
Global Solutions for Incompressible Viscoelastic Fluids
Zhen Lei, Chun Liu, Yi Zhou
We prove the existence of both local and global smooth solutions to the Cauchy problem in the whole space and the periodic problem in the n-dimensional torus for the incompressible…
BKM's Criterion and Global Weak Solutions for Magnetohydrodynamics with Zero Viscosity
Zhen Lei, Yi Zhou
In this paper we derive a criterion for the breakdown of classical solutions to the incompressible magnetohydrodynamic equations with zero viscosity and positive resistivity in $\m…
Logarithmically Improved Criteria for Navier-Stokes Equations
Yi Zhou, Zhen Lei
In this paper we prove the logarithmically improved Serrin's criteria to the three-dimensional incompressible Navier-Stokes equations.