Yin-Xia 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 a weak solution to the three-dimensional magneto-micropolar fluid equations

In this paper, a regularity criterion for the 3D magneto-micropolar fluid equations is investigated. A sufficient condition on the derivative of the velocity field in one direction is obtained. More precisely, we prove that if ux3 belongs to Lβ(0,T;Lα(R3)) with 3α+2β≤1 and α≥3, then the solution (u,v,b) is regular.MSC:35K15, 35K45.

Beale-Kato-Madja type criteria of smooth solutions to 3D Hall-MHD flows

In this article, we study the initial value problem for the impressible Hall-MHD flows in three space dimensions. Several Beale-Kato-Madja type blow up criteria of smooth solutions in term of the vorticity in homogeneous Besov space are established.

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.

Global existence of timelike minimal surface of general co-dimension in Minkowski space time

In this paper, we prove that the global existence of solutions to timelike minimal surface equations having arbitrary co-dimension with slow decay initial data in two space dimensions and three space dimensions, provided that the initial value is suitably small.MSC:35L70.

Blow-up criteria for smooth solutions to the generalized 3D MHD equations

In this paper, we focus on the generalized 3D magnetohydrodynamic equations. Two logarithmically blow-up criteria of smooth solutions are established.MSC:76D03, 76W05.