Zhong Tan

Optimal interior partial regularity for nonlinear elliptic systems under the natural growth condition: The method of A-harmonic approximation

Abstract In this article, the authors consider the nonlinear elliptic systems under the natural growth condition. They use a new method introduced by Duzaar and Grotowski, for proving partial regularity for weak solutions, based on a generalization of the technique of harmonic approximation. And directly establish the optimal Holder exponent for the derivative of a weak solution.

Non-Newton Filtration Equation with special medium void

Abstract This paper considers the existence and asymptotic estimates of global solutions and finite time blowup of local solution of non-Newton filtration equation with special medium void of the following formn u t | x | 2 - Δ p u = u q , ( x , t ) ∈ Ω × ( 0 , T ) , u ( x , t ) = 0 , ( x , t ) ∈ ∂ Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) , u 0 ( x ) ≥ 0 , u 0 ( x ) ≢ 0 , where ρpu = div (|σ u|p−2 σ u) > Ω is a smooth bounded domain in RN(N ≥ 3), 0 ɛ Ω 2 < p < N, p – 1 < q < N p N - p - 1 . The result of asymptotic estimate of global solution depends on the best constant in Hardy inequality.

LPS's Criterion for Incompressible Nematic Liquid Crystal Flows

In this paper we derive LPSs criterion for the breakdown of classical solutions to the incompressible nematic liquid crystal flow, a simplified version of Ericksen-Leslie system modeling the hydrodynamic evolution of nematic liquid crystals in

Energy dissipation for weak solutions of incompressible MHD equations

mathbb R^3

The existence of multiple solutions of p -laplacian elliptic equation

. We show that if

C 1,α -PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS

0<T<+infty

GLOBAL EXISTENCE AND CONVERGENCE RATES OF SMOOTH SOLUTIONS FOR THE 3-D COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITHOUT HEAT CONDUCTIVITY

} is the maximal time interval for the unique smooth solution

Blow-up criterion of classical solutions for the incompressible nematic liquid crystal flows

uin rnC^infty([0,T),mathbb rnR^3)

Weak time-periodic solutions to the compressible navier-stokes equations

, then

Multiplicity results for a nonlinear elliptic problem involving the fractional laplacian

|u|+|nabla d|notin L^q([0,T],L^p(mathbb rnR^3))