Yu-Zhu Wang

Global existence and asymptotic behavior of solutions to a nonlinear wave equation of fourth-order

In this paper we focus on the Cauchy problem for a nonlinear wave equation of fourth-order in n-dimensional space (n ⩾ 1), the decay structure of which is of regularity-loss property. Based on the decay estimate of solutions to the linear problem, we introduce a set of time-weighted Sobolev spaces. By using the contraction mapping theorem, we obtain the global in-time existence and the optimal decay estimates of solutions to the Cauchy problem under smallness assumption on the initial data.

A Beale-Kato-Madja Criterion for Magneto-Micropolar Fluid Equations with Partial Viscosity

We study the incompressible magneto-micropolar fluid equations with partial viscosity in . A blow-up criterion of smooth solutions is obtained. The result is analogous to the celebrated Beale-Kato-Majda type criterion for the inviscid Euler equations of incompressible fluids.

A LOGARITHMALLY IMPROVED BLOW-UP CRITERION OF SMOOTH SOLUTIONS FOR THE THREE-DIMENSIONAL MHD EQUATIONS

In this paper we investigate the Cauchy problem for the three-dimensional incompressible magnetohydrodynamic equations. A logarithmal improved blow-up criterion of smooth solutions is obtained.

Blow-up criterion of smooth solutions for magneto-micropolar fluid equations with partial viscosity

In this paper, we investigate the Cauchy problem for the incompressible magneto-micropolar fluid equations with partial viscosity in ℝn(n = 2, 3). We obtain a Beale-Kato-Majda type blow-up criterion of smooth solutions.MSC (2010): 76D03; 35Q35.

Global existence of classical solutions to the minimal surface equation with slow decay initial value

In this paper, we prove that the global existence of classical solutions to the Cauchy problem for the minimal surface equation with slow decay initial value in Minkowskian space time.

Regularity Criterion for Weak Solution to the 3D Micropolar Fluid Equations

Regularity criterion for the 3D micropolar fluid equations is investigated. We prove that, for some T > 0 , if ∫ 0 T ∥ v x 3 ∥ L ϱ ρ d t ∞ , where 3 / ϱ + 2 / ρ ≤ 1 and ϱ ≥ 3 , then the solution ( v , w ) can be extended smoothly beyond t = T . The derivative v x 3 can be substituted with any directional derivative of v .

Global existence of classical solutions to the minimal surface equation in two space dimensions with slow decay initial value

In this paper, we prove the global existence of classical solutions to the Cauchy problem for the minimal surface equation in the Minkowski space R1+2 with slow decay initial value.

Decay estimate of solutions to the sixth order damped Boussinesq equation

Abstract In this paper, we consider the initial value problem for the sixth order damped Boussinesq equation. We prove the global existence and asymptotic behavior of solutions for all space dimensions n ⩾ 1 provided that the initial value is suitably small. Moreover, we show that the solution can be approximated by the linear solution as time tends to infinity for n ⩾ 2 . The result slightly improves the result obtained by Wang (2012) [3].

Logarithmically improved regularity criteria for the Navier–Stokes equations in Lorentz spaces

Abstract In this paper we investigate three-dimensional incompressible Navier–Stokes equations. We establish some logarithmically improved regularity criteria in term of the Lorentz spaces to the Navier–Stokes equations.