全新正版Zakharov方程及其孤立波解9787030514837科学出版社

1 Physical Background of Zakharov Equations and Its Sollton Solutions
1．1 Transporrces in a Plasma
1．2 System of Equations for Two-Fluid Dynamics
1．3 Solitons in Plasmas
1．3．1 Soliton in Ion Acoustic 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 On the Existence， Blowup and Large Time Behavior of the Zakharov System
2．1 Existence and Uniqueness Theory of the Zakharov System
2．1．1 Weak Solution Theory of Zakharov System
2．1．2 Local Smooth Solution to Zakharov System
2．1．3 Global Smooth Solution to Zakharov System
2．2 Blowup Phenomenon of the Zakharov System
2．2．1 Existence of Self-Similar Blowup Solutions to Zakharov System
2．2．2 Auxiliary Propositions and Lemmas
2．． Existence and Uniqueness of Radially Symmetric Solutions
2．2．4 Concentration Phenomenon of the Blowup Solutions
2．2．5 Nonexistence of Blowup Solutions with Minimum Mass
． Scattering for the Zakharov System in 3D
．．1 Reduction of the System and Linear Decay Estimates
．．2 Energy Estimate
．． Decay Estimate for the Wave Equation
．．4 Weighted Estimates for the Wave Component
．．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 on Generalized Zakharov System
3．1 Zakharov System in Northomogeneous 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 in Two Dimensional Ion-Acoustic Waves
3．4 Zakharov Systems with Magnetic Field Effect
3．4．1 Reduction of Zakharov System with a Magnetic Field
3．4．2 Conservation Laws and Existence of Weak Solutions
3．4．3 Regularized System for the Magnetic Zakharov System
3．4．4 Local Existence Theory of Zakharov System in Cold Plasmas
3．4．5 Local Existence Theory for Zakharov System in Hot 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 ntum Zakharov System
3．5．1 The Main Results
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 Main Results and Introduction of the Strategy
4．2．2 Estimates for Groups and Duhamel Terms
4．． Proof of Global Well-Posedness
4．2．4 Multilinear Estimates
4．3 Low Regularity for Zakharov System in Higher Dimension
4．3．1 Reduction of the System
4．3．2 Estimates of Nonlinear Terms
4．3．3 Well-Posedness of Zakharov System in Higher Dimensions
4．4 Well-Posedness of Two Dimensional Zakharov System
4．4．1 Local Well-Posedness Result
4．4．2 Proof of the Main Theorem
4．4．3 Proof of Multilinear Estimates

5 Singular Limit of Klein——Gordon-Zakharov System with Infinite Propagation Speed
5．1 Introduction
5．2 Preliminary Knowledge
5．2．1 Notations and the Frequency Decoition
5．2．2 Local WeU-Posedness Result
5．． Reduction of the System
5．2．4 Strichartz Norms， Fourier Restriction Norms and Related Estimates
5．3 Bilinear Estimates for Regular Interactions and Non-resonant Interactions
5．4 Energy Estimate on the 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 Main Results
5．7 Convergence in the Energy Space with Small Initial Data

References

评论

This book focuses on the theory of the Zakharov system in the context of plasma physics. It has been over 40 years since the system was first derived by V.E.Zakharov and in course of those decades， many innovative achievements with major impacts on other research fields have been made.
　　The book represents a first attempt to highlight the mathematical theories tharemst important to researchers， including the existence and unique problems， blowup，low regularity， large time behavior and the singular limit. Rather than attempting to examine every aspect of the Zakharov system in detail， it provides an effective road map to help readers access the frontier of studies on this system.

本书适合高等院校高年级大学生和阅读，也适合高校教师和科研人员阅读参考。