关于某类Briot-Bouquet微分方程若干结果的推广

本文研究了某类形式的Briot-Bouquet微分方程的亚纯解结构问题.利用Nevanlinna值分布理论的有关知识,获得了该类微分方程的所有可能形式,以及当方程的阶为偶数时,给出了每一个形式的方程的亚纯解结构,推广了某些特定的Briot-Bouquet微分方程亚纯解结构的一些结果.     

REGULARITY RESULTS FOR LINEAR ELLIPTIC PROBLEMS RELATED TO THE PRIMITIVE EQUATIONS

roductlonWe establish reglllaxlty results for the GFD－Stokes system and some second order ellipticp     

LOGARITHMICALLY IMPROVED REGULARITY CRITERION FOR THE 3D GENERALIZED MAGNETO-HYDRODYNAMIC EQUATIONS

This article proves the logarithmically improved Serrin's criterion for solutions of the 3D generalized magneto-hydrodynamic equations in terms of the gradient of the velocity field, which can be regarded as improvement of results in [10](Luo Y W. On the regularity of generalized MHD equations. J Math Anal Appl, 2010, 365: 806–808) and [18](Zhang Z J.Remarks on the regularity criteria for generalized MHD equations. J Math Anal Appl, 2011,375: 799–802).     

SPIRAL SOLUTION TO THE TWO-DIMENSIONAL TRANSPORT EQUATIONS

The existence of spiral solution for the two-dimensional transport equations is considered in the present paper. Based on the notion of generalized solutions in the sense of Lebesgue-stieltjes integral, the global weak solution of transport equations which includes δ-shocks and vacuum is constructed for some special initial data.     

REGULARITY OF WEAK SOLUTIONS TO MAGNETO-MICROPOLAR FLUID EQUATIONS

In this article,we study the regularity of weak solutions and the blow-up criteria for smooth solutions to the magneto-micropolar fluid equations in R~3.We obtain the classical blow-up criteria for smooth solutions(u,ω,b),i.e.,u ∈ L q(0,T;L p(R 3)) for 2 q + 3 p ≤ 1 with 3p≤∞,u ∈ C([0,T);L 3(R 3)) or u ∈L q(0,T;L p) for 3 2p≤∞ satisfying 2 q + 3p≤2.Moreover,our results indicate that the regularity of weak solutions is dominated by the velocity u of the fluid.In the end-point case p = ∞,the blow-up criteria can be extended to more general spaces u∈ L~1(0,T;B_(∞,∞)~0(R~3)).     

THE GLOBAL L~2 STABILITY OF SOLUTIONS TO THREE DIMENSIONAL MHD EQUATIONS

In this paper,we mainly study the global L2 stability for large solutions to the MHD equations in three-dimensional bounded or unbounded domains.Under suitable conditions of the large solutions,it is shown that the large solutions are stable.And we obtain the equivalent condition of this stability condition.Moreover,the global existence and the stability of two-dimensional MHD equations under three-dimensional perturbations are also established.     

THE BLOW-UP PROPERLIES OF SOLUTIONS TO SEMILINEAR HEAT EQUATIONS WITH NEUMANN BOUNDARY CONDITIONS

1IntroductionInthispaper,weconsidertheinitial-boundaryvalueproblem,where"o(x)isnon-negativesmoothfunctionsatisfying"o.(0)=0,"o.(1)=1'Whenconsideringtheblow-upofsolution,thefollowingproblemarisenaturally:Doesblow-upoccur?Howdoesthesolutionapproachtheblow-uptime'!Andwilersisthehotspotlocated(blow-upset)?WelookattheheatequationwithanonlillearboundaryconditiollHerefiisaboundeddomaininR",p>1isarealnumber.IthasbeenknownforalongtimethattheDroblelil(1.1).(1.2)withAL(~,0)--'no(x)doesnothaveaglobals…     

REMARK ON THE BLOW-UP CRITERION OF STRONG SOLUTIONS TO THE NAVIER-STOKES EQUATIONS IN MULTIPLIER SPACES

In this note, we prove that Xr （0 〈 r 〈 1） norm of the vorticity controls the blow-up phenomena of strong solutions to the Navier-Stokes equations in R3.     

EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR TWO-DIMENSIONAL MODIFIED NAVIER-STOKES EQUATIONS

This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further extended to the case of unbounded channel-like domains.     

复代数微分方程的代数体允许解的一些结果

我们讨论了复代数微分方程的代数体允许解的存在性问题,得到了一些结果.例子表明了定理中的上界是可以达到的.     

A Logarithmically Improved Blow-up Criterion for a Simplified Ericksen-Leslie System Modeling the Liquid Crystal Flows

In this paper, we prove a logarithmically improved blow-up criterion in terms of the homogeneous Besov spaces for a simplified 3D Ericksen-Leslie system modeling the hydrodynamic flow of nematic liquid crystal. The result shows that if a local smooth solution (u,d) satisfies $$∫^T_0\frac{||u||^{\frac{2}{1-r}}_{\dot{B}^{-r}{∞,∞}}+||∇ d||²_{L^∞}}{1+1n(e+||u||_H^S+||∇ d||_H^S)}dt‹∞$$ with 0 ≤ r ‹ 1 and s ≥ 3, then the solution (u,d) can be smoothly extended beyond the time T.     

A NECESSARY AND SUFFICIENT CONDITION FOR GLOBAL EXISTENCE OF CLASSICAL SOLUTIONS TO CAUCHY PROBLEM OF QUASILINEAR HYPERBOLIC SYSTEMS IN DIAGONAL FORM

This article considers Cauchy problem for quasilinear hyperbolic systems in diagonal form.A necessary and sufficient condition in guaranteeing that Cauchy problem admits a unique global classical solution on t 0 is obtained,and a sharp estimate of the life span for the classical solution is given.     

LOCAL WELL-POSEDNESS TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

In this article, we prove the local existence and uniqueness of the classical solution to the Cauchy problem of the 3-D compressible Navier-Stokes equations with large initial data and vacuum, if the shear viscosity μ is a positive constant and the bulk viscosity λ(ρ) = ρβwith β≥ 0. Note that the initial data can be arbitrarily large to contain vacuum states.     

ENTROPY SOLUTIONS FOR FIRST-ORDER QUASILINEAR EQUATIONS RELATED TO A BILATERAL OBSTACLE CONDITION IN A BOUNDED DOMAIN

This paper is devoted to the existence and the uniqueness of the entropy solution for a general scalar conservation law associated with a forced bilateral obstacle condition in a bounded domain of R^P, p ≥ 1. The method of penalization is used with a view to obtaining an existence result. How-ever, the former only gives uniform L^∞-estimates and so leads in fact to look for an Entropy Measure-Valued Solution, according to the specific properties of bounded sequences in L^∞. The uniqueness of this EMVS is proved. Classically, it first ensures the existence of a bounded and measurable function U entropy solution and then the strong convergence in La of approximate solutions to U.     

A Beale–Kato–Majda criterion for the 3D viscous magnetohydrodynamic equations

In this paper, we investigate the Cauchy problem for the 3D viscous incompressible magnetohydrodynamic equations and establish a Beale–Kato–Majda regularity criterion of smooth solutions in terms of the velocity vector in the homogeneous bounded mean oscillations space. Copyright © 2014 John Wiley & Sons, Ltd.     

Non blow-up criterion for the 3-D Magneto-hydrodynamics equations in the limiting case

In this paper, we prove that suitable weak solution(u, b) of the 3-D MHD equations can be extended beyond T if u∈L~∞(0,T; L~3(R~3)) and the horizontal components b_h of the magnetic field satisfies the well-known Ladyzhenskaya-Prodi-Serrin condition, which improves the corresponding regularity criterion by Mahalov-Nicolaenko-Shilkin.     

关于轴对称Navier-Stokes方程正则性的一个注记

建立了一个关于轴对称不可压Navier-Stokes系统的正则性准则.证明了如果局部的轴对称光滑解u满足‖ωr‖_{Lα1((0,T);Lβ1)}+‖ωθ/r‖_{Lα2((0,T);Lβ2)}<∞,其中2/α₁+3/β₁≤1+3/β₁,2/α₂+3/β₂≤2和β₁≥3, β₂>3/2,那么此强解将保持光滑性直至时刻T.     

MULTIPLE POSITIVE SOLUTIONS TO A SYSTEM OF NONLINEAR HAMMERSTEIN TYPE INTEGRAL EQUATIONS

In this paper, we use cone theory and a new method of computation of fixed point index to study a system of nonlinear Hammerstein type integral equations, and the existence of multiple positive solutions to the system is discussed.     

A REMARK ON THE BLOW-UP CRITERION OF STRONG SOLUTIONS AND REGULARITY FOR WEAK SOLUTIONS OF NAVIER-STOKES EQUATIONS

We give blow-up criteria of strong solutions of Navier-Stokes equations with its initial data in Besov spaces and consider the regularity of Leray-Hopf solutions of the equation.