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Global Well-posedness for 3D Generalized Navier-Stokes-Boussinesq Equations

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Acta Mathematicae Applicatae Sinica 2016年第1期32卷 1-16页

作者： quan-sen jiu Huan YU School of Mathematical Sciences Capital Normal University

In this paper,we study the Cauchy problem for the 3D generalized Navier-Stokes-Boussinesq equations with fractional diffusion：{ut＋（u·▽）u＋v∧^2αu=-▽p＋θe3,e3=（0,0,1）^T,θt＋（u·▽）θ=0,Dicu=0. With the help of the smoothing effect of the fractional diffusion operator and a logarithmic estimate,we prove the global well-posedness for this system with α≥5/***,the uniqueness and continuity of the solution with weaker initial data is based on Fourier localization *** results extend ones on the 3D Navier-Stokes equations with fractional diffusion.

关键词： generalized Navier-Stokes-Boussinesq equations global well-posedness uniqueness fourier localization

Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations

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Acta Mathematicae Applicatae Sinica 2007年第4期23卷 637-650页

作者： Xiao-jing Cai quan-sen jiu Chun-yan Xue School of Mathematical Sciences Capital Normal University Beijing 100037 China Department of Mathematics Beijing Information Science and Technology University Beijing 100101 China

In this paper, the Dirichlet problem of Stokes approximate of non-homogeneous incompressible Navier-Stokes equations is studied. It is shown that there exist global weak solutions as well as global and unique strong solution for this problem, under the assumption that initial density po（x） is bounded away from 0 and other appropriate assumptions （see Theorem 1 and Theorem 2）. The semi-Galerkin method is applied to construct the approximate solutions and a prior estimates are made to elaborate upon the compactness of the approximate solutions.

关键词： Non-homogeneous Navier-Stokes equations Stokes approximate weak solutions strong solution

Global L^2 Stability of the Nonhomogeneous Incompressible Navier–Stokes Equations

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Acta Mathematica Sinica,English Series 2013年第11期29卷 2087-2098页

作者： Xiao Jing CAI quan sen jiu Yan Jie ZHOU Department of Mathematics Beijing Technology and Business University Department of Applied Mathematics Beijing University of Technology School of Mathematical Sciences Capital Normal University

In this paper, the problem of the global L^2 stability for large solutions to the nonhomogeneous incompressible Navier-Stokes equations in 3D bounded or unbounded domains is studied. By delicate energy estimates and under the suitable condition of the large solutions, it shows that if the initial data are small perturbation on those of the known strong solutions, the large solutions are stable.

关键词： Nonhomogeneous incompressible Navier-Stokes equations strong solutions stability

Some Remarks on Planar Boussinesq Equations

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Acta Mathematicae Applicatae Sinica 2012年第3期28卷 525-534页

作者： Xiao-jing CAI Chun-yan XUE Xian-jin LI Ying LIU quan-sen jiu Department of Mathematics Beijing Technology and Business UniversityBeijing 100048China College of Applied Sciences Beijing University of TechnologyBeijing 100124China Department of Mathematics Beijing Information Science and Technology UniversityBeijing 100101China Institute of Mechanics Chinese Academy of SciencesBeijing 100190China Fundamental Department of the Academy of Armored Force Engineering Beijing 100072China School of Mathematical Sciences Capital Normal UniversityBeijing 100048China

The main purpose of this paper is to prove the well-posedness of the two-dimensional Boussinesq equations when the initial vorticity wo C L^1 （R^2）（or the finite Radon measure space）. Using the stream function form of the equations and the Schauder fixed-point theorem to get the new proof of these results, we get that when the initial vorticity is smooth, there exists a unique classical solutions for the Cauchy problem of the two dimensional Boussinesq equations.

关键词： Boussinesq equations classical solutions Schauder fixed-point theorem

三维Boussinesq方程组大解的全局L^2稳定性

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数学学报（中文版） 2010年第1期53卷 171-186页

作者：李现今酒全森中国科学院力学研究所北京100190 首都师范大学数学科学学院北京100048

对三维有界及无界区域上的Boussinesq方程的全局L^2稳定性进行了讨论.在解满足适当的条件下,证明了此解为稳定的,并得出此稳定性条件的等价性条件,最后得出了二维Boussinesq方程组在三维扰动下的解的全局存在性和稳定性.

关键词： Boussinesq方程组强解稳定性

Remarks on the Regularity to 3-D Ideal Magnetohydrodynamic Equations

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Acta Mathematicae Applicatae Sinica 2004年第4期 695-708页

作者： quan sen jiu Department of Mathematics,Capital Normal University,Beijing 100037,P.R.China Cheng HE Institute of Applied Mathematics Academy of Mathematics and System Sciences,Chinese Academy of Sciences,Beijing 100080,P.R.China

In this paper we are interested in the sufficient conditions which guarantee the regularityof solutions of 3-D ideal magnetohydrodynamic equations in the arbitrary time interval [0,T].Fivesufficient conditions are *** results are motivated by two main ideas:one is to control theaccumulation of vorticity alone;the other is to generalize the corresponding geometric conditions of3-D Euler equations to 3-D ideal magnetohydrodynamic equations.

关键词： Regular solutions Ideal magnetohydrodynamic equations

Spectral-domain optical coherence tomography in patients with congenital nystagmus

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International Journal of Ophthalmology(English edition) 2011年第6期4卷 627-630页

作者： Hong Yang, jiu-quan Zhang Southwest Eye Hospital Southwest Hospital Third Military Medical University Chongqing 400038 China Department of Radiology Southwest Hospital Third Military Medical University Chongqing 400038 China

AIM: To study macular features in patients with congenital nystagmus and to assess the utility of spectral-domain optical coherence tomography (SD-OCT) in nystagmus. METHODS: The macular areas of 51 outpatients with congenital nystagmus were examined using SD-OCT. Morphological changes in the retinal layers of the macular area were analysed. RESULTS: Macular images were successfully obtained with SD-OCT from 50 (98%) patients. Patients with ocular albinism mainly have macular hypoplasia, abnormal foveal depression, and increased foveal thickness with persistence of an inner nuclear layer, an inner plexiform layer, a ganglion cell layer and a nerve fiber layer. Macular morphology similar to albinism was observed in three patients with idiopathic macular hypoplasia. The OCT findings of cone dystrophy included unclear, disrupted or invisible photoreceptor outer segment/inner segment in the fovea; fusion, thickening and uneven reflection of the outer segment/inner segment with external limiting membrane. Some patients with congenital idiopathic nystagmus showed normal macular morphology and structure, and others showed indistinct macular external limiting membrane reflection. CONCLUSION: SD-OCT is an effective and reliable method to detect the macular morphology of congenital nystagmus patients. This technique has diagnostic value in particular for patients with macular hypoplasia and cone cell dystrophy with no distinct abnormality on fundoscopy.

关键词： optical coherence tomography congenital nystagmus macular disease.

An Analytical Solution for One-Dimensional Water Infiltration and Redistribution in Unsaturated Soil

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Pedosphere 2009年第1期19卷 104-110页

作者： WANG quan-jiu R. HORTON FAN Jun Institute of Water Resources Research Xi＇an University of Technology Xi＇an 710048 （China） State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau Institute of Soil and Water Conservation Chinese Academy of Sciences and Ministry of Water Resources Yangling 712100 （China） Department of Agronomy Iowa State University Ames IA 50011 （USA）

Soil infiltration and redistribution are important processes in field water cycle, and it is necessary to develop a simple model to describe the processes. In this study, an algebraic solution for one-dimensional water infiltration and redistribution without evaporation in unsaturated soil was developed based on Richards equation. The algebraic solution had three parameters, namely, the saturated water conductivity, the comprehensive shape coefficient of the soil water content distribution, and the soil suction allocation coefficient. To analyze the physical features of these parameters, a relationship between the Green-Ampt model and the algebraic solution was established. The three parameters were estimated based on experimental observations, whereas the soil water content and the water infiltration duration were calculated using the algebraic solution. The calculated soil water content and infiltration duration were compared with the experimental observations, and the results indicated that the algebraic solution accurately described the unsaturated soil water flow processes.

关键词： algebraic solution Green-Ampt model soil water infiltration and redistribution unsaturated soil

An Analytical Method for Relationship Between Hydraulic Diffusivity and Soil Sorptivity

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Pedosphere 2006年第4期16卷 444-450页

作者： WANG quan-jiu ZHANG Jiang-Hui FAN Jun State Key Laboratory of Soil Erosion and Dryland Farming on the Loess Plateau Institute of Soil and Water Conservation Chinese Academy of Sciences Yangling 712100 （China） Institute of Water Resources Research Xi＇an University of Technology Xi＇an 710048 （China） Northwest A ＆ F University Yangling 712100 （China）

A simple method was developed to relate soil sorptivity to hydraulic diffusivity and water absorption experiments were conducted utilizing one-dimensional horizontal soil columns to validate the relationship. In addition, an estimation method for hydraulic diffusivity with disc infiltrometer was developed. The results indicated a favorable fit of the theoretical relation to the experimental data. Also, the experiment with disc infiltrometer for estimating the diffusivity showed that the new method was feasible.

关键词： disc infiltrometer hydraulic diffusivity infiltration soil hydraulic parameter sorptivity