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    Zakharov方程及其孤立波解
    丛书名: ISBN: 978-7-03-051483-7
    供应商: 科学出版社 出版日期: 2017年3月1日
    编著者: 本书编委会 译者:
    版次: 1 印次: 1
    页数: 语种:
    纸张: 包装: 精装
    开本: 32开 读者对象:
    原价: ¥138.00 折扣价: ¥99.40    立刻节省:¥38.60
    存量: 现在有货,只剩下7本 销量: 0
       
        
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    内容提要
    This book focuses othe theory of the Zakharov system ithe context of plasma physics. It has beeover 40 years since the system was first derived by V.E.Zakharov and icourse of those decades, many innovative achievements with major impacts oother research fields have beemade.
      The book represents a first attempt to highlight the mathematical theories that are most important to researchers, including the existence and unique problems, blowup,low regularity, large time behavior and the singular limit. Rather thaattempting to examine every aspect of the Zakharov system idetail, it provides aeffective road map to help readers access the frontier of studies othis system.


    目录
    1 Physical Background of Zakharov Equations and Its SolltoSolutions
    1.1 Transport Process ia Plasma
    1.2 System of Equations for Two-Fluid Dynamics
    1.3 Solitons iPlasmas
    1.3.1 SolitoiIoAcoustic Wave
    1.3.2 Langmuir Soliton
    1.3.3 Ls Soliton
    1.3.4 The Light Soliton
    1.3.5 Solitons of Simplified Two-Fluid System

    2 Othe Existence, Blowup and Large Time Behavior of the Zakharov System
    2.1 Existence and Uniqueness Theory of the Zakharov System
    2.1.1 Weak SolutioTheory of Zakharov System
    2.1.2 Local Smooth Solutioto Zakharov System
    2.1.3 Global Smooth Solutioto Zakharov System
    2.2 Blowup Phenomenoof the Zakharov System
    2.2.1 Existence of Self-Similar Blowup Solutions to Zakharov System
    2.2.2 Auxiliary Propositions and Lemmas
    2.2.3 Existence and Uniqueness of Radially Symmetric Solutions
    2.2.4 ConcentratioPhenomenoof the Blowup Solutions
    2.2.5 Nonexistence of Blowup Solutions with Minimum Mass
    2.3 Scattering for the Zakharov System i3D
    2.3.1 Reductioof the System and Linear Decay Estimates
    2.3.2 Energy Estimate
    2.3.3 Decay Estimate for the Wave Equation
    2.3.4 Weighted Estimates for the Wave Component
    2.3.5 Weighted Estimates for the Schr6dinger Component
    2.4 Global Attractors of Dissipative Zakharov System
    2.4.1 Uniform a Priori Estimates
    2.4.2 Existence of Global Attractor

    3 Studies oGeneralized Zakharov System
    3.1 Zakharov System iNorthomogeneous Medium
    3.1.I A Priori Estimates
    3.1.2 Existence and Uniqueness of Global Smooth Solutions
    3.2 Klein——Gordon-Zakharov System
    3.3 Zakharov System iTwo Dimensional Ion-Acoustic Waves
    3.4 Zakharov Systems with Magnetic Field Effect
    3.4.1 Reductioof Zakharov System with a Magnetic Field
    3.4.2 ConservatioLaws and Existence of Weak Solutions
    3.4.3 Regularized System for the Magnetic Zakharov System
    3.4.4 Local Existence Theory of Zakharov System iCold Plasmas
    3.4.5 Local Existence Theory for Zakharov System iHot Plasmas
    3.4.6 Global Existence of Smooth Solutions
    3.4.7 Convergence Behavior of Zakharov System with Magnetic Field Effect
    3.5 Global Well-Posedness for the Quantum Zakharov System
    3.5.1 The MaiResults
    3.5.2 Some Energy Estimates for the Solution
    3.5.3 Proof of the Global Well-Posedness Result
    3.5.4 Proof of the Classic Limit Behavior

    4 Low Regularity Theories of Zakharov System
    4.1 Preliminaries
    4.1.1 Work Space
    4.1.2 Linear Estimates
    4.2 Global Well-Posedness for One Dimensional Zakharov System
    4.2.1 MaiResults and Introductioof the Strategy
    4.2.2 Estimates for Groups and Duhamel Terms
    4.2.3 Proof of Global Well-Posedness
    4.2.4 Multilinear Estimates
    4.3 Low Regularity for Zakharov System iHigher Dimension
    4.3.1 Reductioof the System
    4.3.2 Estimates of Nonlinear Terms
    4.3.3 Well-Posedness of Zakharov System iHigher Dimensions
    4.4 Well-Posedness of Two Dimensional Zakharov System
    4.4.1 Local Well-Posedness Result
    4.4.2 Proof of the MaiTheorem
    4.4.3 Proof of Multilinear Estimates

    5 Singular Limit of Klein——Gordon-Zakharov System with Infinite PropagatioSpeed
    5.1 Introduction
    5.2 Preliminary Knowledge
    5.2.1 Notations and the Frequency Decomposition
    5.2.2 Local WeU-Posedness Result
    5.2.3 Reductioof the System
    5.2.4 Strichartz Norms, Fourier RestrictioNorms and Related Estimates
    5.3 Bilinear Estimates for Regular Interactions and Non-resonant Interactions
    5.4 Energy Estimate othe Resonant Components
    5.5 Convergence Results
    5.5.1 Limit Behavior of the Klein-Gordon-Zakharov System
    5.5.2 Uniform Bounds and Two Lemmas
    5.6 Proof of the MaiResults
    5.7 Convergence ithe Energy Space with Small Initial Data

    References
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