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Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases

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Science China mathematics 2010年第3期53卷 719-738页

作者： KONG DeXing 1 , LIU KeFeng 2 & WANG YuZhu 3, 1 department of mathematics, Zhejiang university, Hangzhou 310027, China 2.department of mathematics, university of California at Los Angeles, CA 90095, usa 3 department of mathematics, Shanghai Jiao Tong university, Shanghai 200248, China 1. department of mathematics Zhejiang University Hangzhou 310027 China2. Department of Mathematics University of California at Los Angeles Los Angeles CA 90095 USA3. Department of Mathematics Shanghai Jiao Tong University Shanghai 200248 China

In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.

关键词： Chaplygin gases compressible Euler equations irrotational flow null condition Cauchy problem smooth solution

GLOBAL DYNAMICS OF DISSIPATIVE GENERALIZED KORTEWEG-DE VRIES EQUATIONS

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Chinese Annals of mathematics,Series B 1996年第4期17卷 389-402页

作者：尤云程 UNIV S florida DEPT MATHTAMPAFL 33620

This work deals with the dissipative generalized Korteweg-de Vries (gKdV) equations of the formu t + u 2u x + u xxx-bu xx+ ru = f, t≥0, u(0,x) = u 0(x)∈V = H 2 2π,with periodic boundary conditions. It is proved that there exists an inertial manifold for the semiflow generated by this equation in space V. Since such a manifold is finite dimensional, positively invariant, and exponentially attracting of all the solution trajectories, the long-time dynamics of the dissipative gKdV equations are determined by a finite number of modes without the soliton phenomena.

关键词： Dissipative generalized KdV equation Global dynamics Inertial manifold Soliton

Troponin I, cardiac diastolic dysfunction and restrictive cardiomyopathy

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Acta Pharmacologica Sinica 2004年第12期25卷 3-9页

作者： Xu-pei HUANG2, Jian-feng DU department of Biomedical Science, Centerfor Molecular Biologyand Biotechnology, florida Atlanticuniversity, Boca Raton, fl 33431, usa department of Biomedical Science Center for Molecular Biology and Biotechnology Florida Atlantic University Boca Raton FL 33431 US

Cardiomyopathies are diseases of heart muscle that are associated with cardiac dysfunction. Molecular ge- netic studies performed to date have demonstrated that the damage or mutations in several sarcomeric contractile protein genes are associated with the development of the diseases. In this review, cardiac troponin I, one of the sarcomeric thin filament protein, will be discussed regarding its role in cardiac function, its deficiency-related diastolic dysfunction, and the mutation of this protein-mediated restrictive cardiomyopathy.

关键词： troponin I restrictive cardiomyopathy contractile proteins missense mutation diastole genetically modified animals cardiology

Quasisymmetric property for conjugacies between Anosov diffeomorphisms of the two-torus

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Science China mathematics 2010年第3期53卷 663-670页

作者： HU HuYi 1 & JIANG YunPing 2, 1 department of mathematics, Michigan State university, East Lansing, MI 48824, usa 2.department of mathematics, the Graduate Center and Queens College of CUNY, flushing, NY 11367, usa 1. department of mathematics Michigan State University East Lansing MI 48824 USA2. Department of Mathematics the Graduate Center and Queens College of CUNY Flushing NY 11367 USA

We prove that the restrictions of the conjugacy between two Anosov diffeomorphisms of the twotorus to the stable and unstable manifolds are quasisymmetric homeomorphisms.

关键词： quasisymmetry Anosov diffeomorphisms conjugacy Hlder condition Markov partition

Littlewood-Paley operators with variable kernels

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Science China mathematics 2006年第5期49卷 639-650页

作者： CHEN Jiecheng, DING Yong & FAN Dashan department of mathematics, Zhejiang university (Xixi Campus), Hangzhou 310028, China School of Mathematical Sciences, Beijing Normal university, Beijing 100875, China department of mathematics, university of Wisconsin-Milwaukee, Milwaukee WI 53201, usa department of mathematics, central China Normal university, Wuhan 430074, China department of mathematics Zhejiang University [Xixi Campus] Hangzhou 310028 China School of Mathematical Sciences Beijing Normal University Beijing 100875 China department of mathematics University of Wisconsin-Milwaukee Milwaukee WI 53201 USA department of mathematics Central China Normal University Wuhan 430074 China

In this paper we study a certain directional Hilbert transform and the boundedness on some mixed norm spaces. As one of applications, we prove the Lp-boundedness of the Littlewood-Paley operators with variable kernels... 详细信息

关键词： directional Hilbert transform, Sobolev spaces, Littlewood-Paley operator,variable kernel.

Polynomials,Higher Order Sobolev Extension Theorems and Interpolation Inequalities on Weighted Folland-Stein Spaces on Stratified Groups

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Acta Mathematica Sinica,English Series 2000年第3期16卷 405-444页

作者： Guozhen Lu department of mathematics,Wayne State university,Detroit,MI 48202,usa department of mathematics Wayne State University Detroit USA

This paper consists of three main *** of them is to develop local and global Sobolev interpolation inequalities of any higher order for the nonisotropic Sobolev spaces on stratified nilpotent Lie *** the extensive research after Jerison’s work[3]on Poincaré-type inequalities for Hrmander’s vector fields over the years,our results given here even in the nonweighted case appear to be *** interpolation inequalities have crucial applications to subelliptic or parabolic PDE’s involving vector *** main tools to prove such inequalities are approximating the Sobolev func- tions by polynomials associated with the left invariant vector fields on *** very useful properties for polynomials associated with the functions are given here and they appear to have independent interests in their own *** the existence of such polynomials is the second main part of this *** results of these two parts have been announced in the author’s paper in Mathematical Research Letters[38]. The third main part of this paper contains extension theorems on anisotropic Sobolev spaces on stratified groups and their applications to proving Sobolev interpolation inequalities on(εδ)domains. Some results of weighted Sobolev spaces are also given *** construct a linear extension operator which is bounded on different Sobolev spaces *** particular,we are able to construct a bounded linear extension operator such that the derivatives of the extended function can be controlled by the same order of derivatives of the given Sobolev *** are stated and proved for weighted anisotropic Sobolev spaces on stratified groups.

关键词： Poincaré inequalities Extension theorems Interpolation inequalities Anisotropic Sobolev spaces A_p weights (ε,δ)domains Vector fields Polynomials on stratified groups

Discrete Calderón-type Reproducing Formula

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Acta Mathematica Sinica,English Series 2000年第2期16卷 277-294页

作者： Yongsheng Han department of mathematics,Auburn university,Auburn,Alabama 36849-5310,usa department of mathematics Auburn University Auburn Alabama 36849-5310 USA

In this paper we use the Calderón-Zygmund operator theory to provide a discrete Calderón- type reproducing *** translation,dilation and,in particular,the Fourier transform are never used in the proofs,all results still hold on spaces of homogeneous type introduced by Coifman and Weiss. As a consequence,we obtain a class of frames with the minimum regularity properties.

关键词： Spaces of homogeneous type Calderón reproducing formula Frame

SYMPLECTIC SCHEMES FOR QUASILINEAR WAVE EQUATIONS OF KLEIN-GORDON AND SINE-GORDON TYPE

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Journal of Computational mathematics 2001年第5期19卷 475-488页

作者： Xiao-wu Lu (department of mathematics and Computer Science, Emory university, Atlanta, GA 30322, usa) Emory university 美国 30322

Presents a class of finite difference methods of first and second order accuracy for the computation of solutions to the quasilinear wave equations. Overview of general symplectic schemes and generating functional; Nu... 详细信息

关键词： Symplectic integration Sine-Gordon equations Finite difference method.

Equivalence problem for Bishop surfaces

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Science China mathematics 2010年第3期53卷 687-700页

作者： HUANG XiaoJun 1, & YIN WanKe 2 1 department of mathematics, Rutgers university, New Brunswick, NJ 08902, usa 2 School of mathematics and Statistics, Wuhan university, Wuhan 430072, China 1. department of mathematics Rutgers University New Brunswick NJ 08902 USA2. School of Mathematics and Statistics Wuhan University Wuhan 430072 China

The paper has two parts. We first briefly survey recent studies on the equivalence problem for real submanifolds in a complex space under the action of biholomorphic transformations. We will mainly focus on some of the recent studies of Bishop surfaces, which, in particular, includes the work of the authors. In the second part of the paper, we apply the general theory developed by the authors to explicitly classify an algebraic family of Bishop surfaces with a vanishing Bishop invariant. More precisely, we let M be a real submanifold of C 2 defined by an equation of the form w = zz + 2Re(z s + az s+1 ) with s≥ 3 and a a complex parameter. We will prove in the second part of the paper that for s≥ 4 two such surfaces are holomorphically equivalent if and only if the parameter differs by a certain rotation. When s = 3, we show that surfaces of this type with two different real parameters are not holomorphically equivalent.

关键词： equivalence problem Bishop surface Chern-Moser theory elliptic and hyperbolic complex tangents normal form and modular space