Some properties of a class of abstract stationary equations

We study a class of abstract nonlinear equations in a separable Hilbert space for which we prove some generic properties of the set of solutions. The results apply, in particular, in several models of hydrodynamics, such as magneto-micropolar equations, micropolar fluid equations, Boussinesq and Navier–Stokes equations.     

半导体漂移 扩散方程稳态解的存在性

考虑半导体方程稳态模型的混合边值问题，应用Schauder不动点定理证明了逼近解的存在性，通过一系列先验估计的获得，利用紧致性原理证明了稳态解的存在性.     

The stationary three‐dimensional Navier–Stokes equations with a non‐zero constant velocity at infinity

This paper is devoted to some mathematical questions related to the three‐dimensional stationary Navier–Stokes equations. Our approach is based on a combination of properties of Oseen problems in ?³. Copyright © 2008 John Wiley & Sons, Ltd.     

带雪崩项半导体方程稳态解的存在性

考虑带雪崩项半导体方程稳态模型的混合边值问题，应用Schauder不动点定理证明了逼近解的存在性，通过一系列先验估计的获得，利用紧致性原理证明了稳态弱解的存在性．     

Irregular scaling functions with orthogonal translations

For all integers m,k>1 with m≡1modk we construct, among others, a function with dense graph in the set [0,k]×R such that

     

Quasilinear elliptic equations with subquadratic growth

In this paper we consider nonlinear boundary value problems whose simplest model is the following:

(0.1)     

On partial regularity of suitable weak solutions to the stationary fractional Navier–Stokes equations in dimension four and five

In this paper, we investigate the partial regularity of suitable weak solutions to the multidimensional stationary Navier Stokes equations with fractional power of the Laplacian (-△)~α 1 and α≠ 1/2). It is shown that the n + 2-6α(3 ≤ n ≤ 5) dimensional Hausdorff measure of the set of the possible singular points of suitable weak solutions to the system is zero, which extends a recent result of Tang and Yu [19] to four and five dimension. Moreover, the pressure in e-regularity criteria is an improvement of corresponding results in [1, 13, 18, 20].     

外部流动的Oseen耦合方法,I:Oseen耦合逼近

这篇文章考虑了具有非齐次边界条件的二维非定常外部Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程．通过将内部区域的Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程和外部区域的Ｏｓｅｅｎ方程相耦合,得到了Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ问题的逼近问题： Ｏｓｅｅｎ耦合问题,此外,我们证明了 Ｏｓｅｅｎ耦合方程弱解的存在性,唯一性和收敛精度．     

Oseen Coupling Method for the Exterior Flow Part I: Oseen Coupling Approximation

Abstract In this paper, we consider the bidimensional exterior unsteady Navier-Stokes equations with nonhomogeneous boundary conditions and present an Oseen coupling problem which approximates the Navier-Stokes problem, obtained by coupling the Navier-Stokes equations in the inner region and the Oseen equations in the outer region. Moreover, we prove the existence, uniqueness and the approximate accuracy of the weak solution of the Oseen coupling equations. Project supported by NSF of China & State Major Key Project of Basic Research     

单位球上不同Hardy空间之间的乘法算子

作者研究了C^N 中单位球B上不同Hardy空间之间的乘法算子, 给出了有界的乘法算子M_g: H^p(B) → H^q(B)$的特征.     

Duals of Hardy Spaces of B-valued Martingales for 0<r≤1

The dual of B-valued martingale Hardy space Hs(p)r(B) with small index 0 r ≤ 1,which is associated with the conditional p-variation of B-valued martingale,is characterized.In order to obtain the results,a new type of Campanato spaces for B-valued martingales is introduced and the classical technique of atomic decompositions is improved.Some results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of the underlying Banach space.     

热方程的一些端点估计及其在Navier-Stokes方程中的应用——献给陆善镇教授75华诞

本文首先讨论热方程初值问题的解在Hardy、BMO（bounded mean oscillation）和Besov型空间中的估计.然后本文结合Coifmann-Lions-Meyer-Semmes在Hardy空间中的补偿紧性结果,给出Navier-Stokes方程整体弱解的二阶导数的一些端点估计.     

A note on Besov-Morrey spaces and Triebel-Lizorkin-Morrey spaces

In the present paper, we obtain three independent results on the Besov-Morrey spaces and the Triebel-Lizorkin-Morrey spaces. That is, we are going to obtain the characterization of local means, the boundedness of pseudo-differential operators and the characterization of the Hardy-Morrey spaces. By using the maximal estimate and the molecular decomposition, we shall integrate and extend the known results on these spaces.     

Hardy spaces and partial derivatives of conjugate harmonic functions

In this paper we give necessary and sufficient conditions for a harmonic vector and all its partial derivatives to belong to for all .