PARTIAL REGULARITY FOR STATIONARY NAVIER-STOKES SYSTEMS BY THE METHOD OF A-HARMONIC APPROXIMATION

In this article, we prove a regularity result for weak solutions away from singular set of stationary Navier-Stokes systems with subquadratic growth under controllable growth condition. The proof is based on the A-harmonic approximation technique. In this article,we extend the result of Shuhong Chen and Zhong Tan [7] and Giaquinta and Modica [18] to the stationary Navier-Stokes system with subquadratic growth.     

PARTIAL REGULARITY RESULT OF SUPERQUADRATIC ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

We consider the partial regularity for weak solutions to superquadratic elliptic systems with controllable growth condition, under the assumption of Dini continuous coefficients. The proof relies upon an iteration scheme of a decay estimate for a new type of excess functional. To establish the decay estimate, we use the technique of A-harmonic approximation and obtain a general criterion for a weak solution to be regular in the neighborhood of a given point. In particular, the proof yields directly the optimal H¨older exponent for the derivative of the weak solutions on the regular set.     

REGULARITY THEORY FOR SYSTEMS OF PARTIAL DIFFERENTIAL EQUATIONS WITHN EUMANN BOUNDARY CONDITIONS

Inroductlonu consider here a system     

STATIONARY OSCILLATIONS OF SECOND ORDER PERIODIC SYSTEMS UNDER STOCHASTIC NOISE INTERFERENCE

ＳＴＡＴＩＯＮＡＲＹＯＳＣＩＬＬＡＴＩＯＮＳＯＦＳＥＣＯＮＤＯＲＤＥＲＰＥＲＩＯＤＩＣＳＹＳＴＥＭＳＵＮＤＥＲＳＴＯＣＨＡＳＴＩＣＮＯＩＳＥＩＮＴＥＲＦＥＲＥＮＣＥ￥ＤｅｎｇＦｅｉｑｉ（ＮｏｒｔｈｅａｓｔＩｎｓｔｉｔｕｔｅｏｆＨｅａｖｙＭａｃｈｉｎｅ...     

具间断系数拟线性退化椭圆方程在可控增长下的正则性

对于具有VMO间断系数的散度型拟线性退化椭圆型方程,考虑了低阶项微分项在可控制增长条件下的弱解梯度的Morrey空间L^p,λ局部正则性,从而在已知数据正则性提高的条件下得到弱解具有优化Hlder指数的Hlder连续性结果。     

奖惩系统在随机优序下的极小与极大平稳分布

奖惩系统(Bonus-M a lus System)是世界各国机动车辆险中广泛采用的一种经验费率厘定机制.文[1]在最一般的框架下,给出了奖惩系统的数学建模与稳态分析.本文将进一步证明,文[1]中给出的奖惩系统两种特定的平稳分布恰分别是奖惩系统在随机优序下的极小与极大平稳分布.特别地,基于这一事实严格证明了文[1]提出的有关封闭型奖惩系统年度总保费的一个猜想.     

区间周期系统的平稳振荡

本文给出了区间周期系统平稳振荡的概念，建立了区间矩阵稳定性与区间周期系统平稳振荡之间的关系，推广和改进了文[1]的结果．     

OPTIMAL INTERIOR PARTIAL REGULARITY FOR NONLINEAR ELLIPTIC SYSTEMS WITH DINI CONTINUOUS COEFFICIENTS

In this article,we consider nonlinear elliptic systems of divergence type with Dini continuous coefficients.The authors use a new method introduced by Duzaar and Grotowski,to prove partial regularity for weak solutions,based on a generalization of the technique of harmonic approximation and directly establish the optimal Ho¨lder exponent for the derivative of a weak solution on its regular set.     

STATIONARY OSCILLATIONS OF LARGE-SCALE NONLINEAR TIME-DELAY SYSTEMS

ＳＴＡＴＩＯＮＡＲＹＯＳＣＩＬＬＡＴＩＯＮＳＯＦＬＡＲＧＥ－ＳＣＡＬＥＮＯＮＬＩＮＥＡＲＴＩＭＥ－ＤＥＬＡＹＳＹＳＴＥＭＳＤｅｎｇＦｅｉｑｉ（邓飞其）（ＮｏｒｔｈｅａｓｔＩｎｓｔｉｔｕｔｅｏｆＨｅａｖｙＭａｃｈｉｎｅｒｙ）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉ...     

定常Navier-Stokes方程有限元分析

的近似解.方程(1.1)中的Γ是区域Ω(R~N)的边界.假设Γ充分光滑,在适当条件下,上述问题的解(u,p)(∈(H_0~1)(Ω))~N×L_0~2(Ω))是存在唯一的.关于H_0~1(Ω),L_0~2(Ω)等记号将在下面统一说明.Falk曾用Galerkin-Langrange乘子法找Stokes问题的近似解,近似解空间(V_(1h)~0)~N×X_h取为(H_0~1(Ω))~N×L~2(Ω)的有限维子空间.[3]中指出,当Ω不是多角形区域时,构造H_0~1(Ω)且满足一定条件的有限维子空间V_(1h)~0是比较复杂     

Navier-Stokes方程正则性和爆破的一类条件

考虑3维的Navier-Stokes方程.当2/s+3/q=2-α,q＞1,1＜α+3/q＜2且解的涡度ω=curlu满足∫T0(∫R3(|x-x0|αω)qdx)s/q dt＜∞时,则∫T0∫R3|x-x01-1/2|▽ω|2dxdt＜∞,特别地,解是正则的.若在T*处有∫T*0(∫R3(|x-x0|αω)qdx)s/q dt=∞,则解在此处爆破.这是Navier-Stokes方程正则性判别准则在加权情形的一个新结果.     

REGULARITY FOR CERTAIN QUASILINEAR ELLIPTIC SYSTEMS OF DIVERGENCE STRUCTURE

1 IntroductionEnter section title between curly braces In [1], partiaJ H6lder continuity of the gradient ofsolution to elliptic systems of the formunder the assumption that the solutions u E C',,(O). In general, we can only obtain the Co,o-regularity see [2]-[6]. Under strong assumption can we obtain Co,l- regularity t see f7J. In thepresent paper a partial COl"-regularity and E- regularity theorem are derived fOr the gradientof solutions of elliptic systems of the formin a domain fl in …     

LARGE TIME ASYMPTOTIC BEHAVIOR OF THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN PARTIAL SPACE-PERIODIC DOMAINS

In this article, we study the large time behavior of the 3-D isentropic compressible Navier-Stokes equation in the partial space-periodic domains, and simultaneously show that the related profile systems can be described by like Navier-Stokes equations with suitable"pressure" functions in lower dimensions. Our proofs are based on the energy methods together with some delicate analysis on the corresponding linearized problems.     

GLOBAL REGULARITY OF 2D INCOMPRESSIBLE MAGNETO-MICROPOLAR FLUID EQUATIONS WITH PARTIAL VISCOSITY

This paper studies the global regularity of 2D incompressible anisotropic magnetomicropolar fluid equations with partial viscosity. Ma [22](Ma L. Nonlinear Anal: Real World Appl, 2018, 40: 95–129) examined the global regularity of the 2D incompressible magnetomicropolar fluid system for 21 anisotropic partial viscosity cases. He proved the global existence of a classical solution for some cases and established the conditional global regularity for some other cases. In this paper, we also investi...     

二维Navier-Stokes方程同位有限体积法的稳定性改进

1 引言 考虑不可压缩粘性流体的二维Navier-Stokes方程,它由速度压力公式和连续性方程的耦合组成.     

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.     

偏泛函微分方程系统解的强迫振动性

本文研究两类偏泛函微分方程系统的强迫振动性.建立了这两类偏泛函微分方程系统解的强迫振动的若干判据.     

平稳正态序列超过数点过程与部分和的渐近联合分布

{Xi}为平稳正态序列,具有EX1=0,EX12=1,ρn=EX1Xn 1.对于水平un= ,记在 的条件下,得到了Nn(B)与Sn的渐近联合分布,同时也给出了极值与Sn的渐近联合分布.     

具有临界指数的半线性椭圆组弱解的正则性

本文研究具有临界指数的方程组。用ＤｅＧｉｏｒｇｅ估计方法，获得方程组的解的有界性。     

SEMI-LINEAR SYSTEMS OF BACKWARD STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS IN R~n

This paper explores the diffeomorphism of a backward stochastic ordinary differential equation (BSDE) to a system of semi-linear backward stochastic partial differential equations (BSPDEs), under the inverse of a stochastic flow generated by an ordinary stochastic differential equation (SDE). The author develops a new approach to BSPDEs and also provides some new results. The adapted solution of BSPDEs in terms of those of SDEs and BSDEs is constructed. This brings a new insight on BSPDEs, and leads to a probabilistic approach. As a consequence, the existence, uniqueness, and regularity results are obtained for the (classical, Sobolev, and distributional) solution of BSPDEs. The dimension of the space variable x is allowed to be arbitrary n, and BSPDEs are allowed to be nonlinear in both unknown variables, which implies that the BSPDEs may be nonlinear in the gradient. Due to the limitation of space, however, this paper concerns only classical solution of BSPDEs under some more restricted assumptions.