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- Thomas Y. Hou, Zhen Lei
- 2008

We investigate the stabilizing effect of convection in three-dimensional incompressible Euler and Navier-Stokes equations. The convection term is the main source of nonlinearity for these equations.â€¦ (More)

- Zhen Lei, Chun Liu, Yi Fan Zhou
- 2009

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 viscoelasticâ€¦ (More)

- Thomas Y. Hou, Zhen Lei
- 2008

We investigate the stabilizing effect of convection in 3D incompressible Euler and NavierStokes equations. The convection term is the main source of nonlinearity for these equations. It is oftenâ€¦ (More)

Yongyong Cai,1 Matthias Rosenkranz,1,* Zhen Lei,2,3,4 and Weizhu Bao1,5,â€ 1Department of Mathematics, National University of Singapore, 119076, Singapore 2School of Mathematical Sciences, Fudanâ€¦ (More)

- Zhen Lei, Yi Fan Zhou
- 2009

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 R3. This result isâ€¦ (More)

- Yi Fan Zhou, Zhen Lei
- 2008

In this paper we prove the global existence and uniqueness of the low regularity solutions to the Cauchy problem of quasi-linear wave equations with radial symmetric initial data in three spaceâ€¦ (More)

- Zhen Lei, Yuxi Zheng
- 2006

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 of gas of constantâ€¦ (More)

- Thomas Y. Hou, Zhen Lei, Congming Li
- 2007

In this paper, we study the 3D axisymmetric Navier-Stokes Equations with swirl. We prove the global regularity of the 3D Navier-Stokes equations for a family of large anisotropic initial data.â€¦ (More)

- Yi Fan Zhou, Zhen Lei
- 2008

In this paper we prove the logarithmically improved Beale-Kato-Majda's criterion to the three-dimensional incompressible Euler and Navier-Stokes equations as well as the logarithmically improvedâ€¦ (More)

- Thomas Y. Hou, Zhen Lei, Guo Luo, Shu Wang, Chen Zou
- 2013

In (Comm Pure Appl Math 62(4):502â€“564, 2009), Hou and Lei proposed a 3D model for the axisymmetric incompressible Euler and Navierâ€“Stokes equations with swirl. This model shares a number ofâ€¦ (More)