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LOCAL EXISTENCE AND UNIQUENESS OF STRONG SOLUTIONS TO THE TWO DIMENSIONAL NONHOMOGENEOUS INCOMPRESSIBLE PRIMITIVE EQUATIONS

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Acta Mathematica Scientia 2020年第5期40卷 1316-1334页

作者： Quansen JIU Fengchao WANG School of Mathematical Sciences Capital Normal UniversityBeijing 10004&China Advanced Institute of Natural Sciences Beijing Normal University at ZhuhaiZhuhai 519087China School of Mathematical Sciences Beijing Normal University and Key Laboratory of Mathematics and Complex SystemsMinistry of Education Beijing 100875China

In this article,we study the initial boundary value problem of the two-dimensional nonhomogeneous incompressible primitive equations and obtain the local existence and uniqueness of strong *** initial vacuum is allowed.

关键词： local existence and uniqueness strong solutions nonhomogeneous incompressible primitive equations

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Consensus control of multi-manipulator systems based on disturbance observer under Markov switching topologies

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Control Theory and Technology 2021年第2期19卷 273-282页

作者： Chang-E Ren Quanxin Fu College of Information Engineering Capital Normal UniversityBeijing100089China

In this paper,to solve the consensus control problem of multi-manipulator systems under Markov switching topologies,we propose a distributed consensus control strategy based on disturbance *** multi-manipulator systems,external disturbance described by heterogeneous exogenous systems is considered,and all communication topologies are ***,a disturbance observer is presented to suppress the influence of unknown external disturbance,and the equivalent compensation is introduced into the control protocol in multi-manipulator ***,a novel control protocol based on neighbor information is designed,which guarantees that multi-manipulator systems reach consensus under Markov switching ***,two simulation examples verify the validity of the theoretical result.

关键词： Multi-manipulator systems Disturbance observer Markov switching topologies Consensus control

Global existence of weak solutions to the drift-flux system for general pressure laws

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Science China Mathematics 2023年第2期66卷 251-284页

作者： Hailiang Li Lingyun Shou School of Mathematical Sciences Capital Normal UniversityBeijing 100048China academy for multidisciplinary studies Capital Normal UniversityBeijing 100048China

The initial value problem of the multi-dimensional drift-flux model for two-phase flow is investigated in this paper,and the global existence of weak solutions with finite energy is established for general pressure-de... 详细信息

关键词： two-phase flow drift-flux model global weak solution non-monotone pressure law quantitative regularity estimate

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Global existence and large-time behavior for primitive equations with the free boundary

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Science China Mathematics 2024年第10期67卷 2303-2330页

作者： Hai-Liang Li Chuangchuang Liang School of Mathematical Sciences Capital Normal UniversityBeijing 100048China academy for multidisciplinary studies Capital Normal UniversityBeijing 100048China College of Mathematics and Statistics Chongqing UniversityChongqing 401331China

In the present paper, the primitive equations, which can be used to simulate the large-scale motion of the ocean and atmosphere, are considered in the three-dimensional domain bounded below by a fixed solid boundary and above by a free-moving boundary. The global existence and uniqueness of strong solutions are established, and the long-time convergence to the equilibrium state is shown to be either at an exponential rate for the horizontal periodic domain or at an algebraic rate for the horizontal whole space.

关键词： primitive equations the free boundary value problem global well-posedness large-time behavior

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Hyperbolic Properties of Geodesic Flows on Certain Manifolds without Conjugate Points

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Acta Mathematica Sinica,English Series 2024年

作者： Fei LIU Xiaokai LIU Fang WANG College of Mathematics and Systems Science Shandong University of Science and Technology Department of Mathematics Southern University of Science and Technology School of Mathematical Sciences Capital Normal University

In this article, we study the hyperbolic dynamics of geodesic flows on Riemannian (not necessarily compact) manifolds with no conjugate points. By hyperbolic dynamics, we focus on the Anosov Closing Lemma, the local product structure, and the transitivity of the geodesic flows on the set of rank 1non-wandering set?1 under the conditions of bounded asymptote and uniform visibility. As an application,we further discuss on some generic properties of the set of invariant probability measures.

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