Zakharov·½³Ì¼°Æä¹ÂÁ¢²¨½â

1 Physical Background of Zakharov Equations and Its Sollton Solutions1£®1 Transport Process in a Plasma1£®2 System of Equations for Two-Fluid Dynamics1£®3 Solitons in Plasmas1£®3£®1 Soliton in Ion Acoustic Wave1£®3£®2 Langmuir Soliton1£®3£®3 Ls Soliton1£®3£®4 The Light Soliton1£®3£®5 Solitons of Simplified Two-Fluid System2 On the Existence£¬ Blowup and Large Time Behavior of the Zakharov System2£®1 Existence and Uniqueness Theory of the Zakharov System2£®1£®1 Weak Solution Theory of Zakharov System2£®1£®2 Local Smooth Solution to Zakharov System2£®1£®3 Global Smooth Solution to Zakharov System2£®2 Blowup Phenomenon of the Zakharov System2£®2£®1 Existence of Self-Similar Blowup Solutions to Zakharov System2£®2£®2 Auxiliary Propositions and Lemmas2£®2£®3 Existence and Uniqueness of Radially Symmetric Solutions2£®2£®4 Concentration Phenomenon of the Blowup Solutions2£®2£®5 Nonexistence of Blowup Solutions with Minimum Mass2£®3 Scattering for the Zakharov System in 3D2£®3£®1 Reduction of the System and Linear Decay Estimates2£®3£®2 Energy Estimate2£®3£®3 Decay Estimate for the Wave Equation2£®3£®4 Weighted Estimates for the Wave Component2£®3£®5 Weighted Estimates for the Schr6dinger Component2£®4 Global Attractors of Dissipative Zakharov System2£®4£®1 Uniform a Priori Estimates2£®4£®2 Existence of Global Attractor3 Studies on Generalized Zakharov System3£®1 Zakharov System in Northomogeneous Medium3£®1£®I A Priori Estimates3£®1£®2 Existence and Uniqueness of Global Smooth Solutions3£®2 Klein¡ª¡ªGordon-Zakharov System3£®3 Zakharov System in Two Dimensional Ion-Acoustic Waves3£®4 Zakharov Systems with Magnetic Field Effect3£®4£®1 Reduction of Zakharov System with a Magnetic Field3£®4£®2 Conservation Laws and Existence of Weak Solutions3£®4£®3 Regularized System for the Magnetic Zakharov System3£®4£®4 Local Existence Theory of Zakharov System in Cold Plasmas3£®4£®5 Local Existence Theory for Zakharov System in Hot Plasmas3£®4£®6 Global Existence of Smooth Solutions3£®4£®7 Convergence Behavior of Zakharov System with Magnetic Field Effect3£®5 Global Well-Posedness for the Quantum Zakharov System3£®5£®1 The Main Results3£®5£®2 Some Energy Estimates for the Solution3£®5£®3 Proof of the Global Well-Posedness Result3£®5£®4 Proof of the Classic Limit Behavior4 Low Regularity Theories of Zakharov System4£®1 Preliminaries4£®1£®1 Work Space4£®1£®2 Linear Estimates4£®2 Global Well-Posedness for One Dimensional Zakharov System4£®2£®1 Main Results and Introduction of the Strategy4£®2£®2 Estimates for Groups and Duhamel Terms4£®2£®3 Proof of Global Well-Posedness4£®2£®4 Multilinear Estimates4£®3 Low Regularity for Zakharov System in Higher Dimension4£®3£®1 Reduction of the System4£®3£®2 Estimates of Nonlinear Terms4£®3£®3 Well-Posedness of Zakharov System in Higher Dimensions4£®4 Well-Posedness of Two Dimensional Zakharov System4£®4£®1 Local Well-Posedness Result4£®4£®2 Proof of the Main Theorem4£®4£®3 Proof of Multilinear Estimates5 Singular Limit of Klein¡ª¡ªGordon-Zakharov System with Infinite Propagation Speed5£®1 Introduction5£®2 Preliminary Knowledge5£®2£®1 Notations and the Frequency Decomposition5£®2£®2 Local WeU-Posedness Result5£®2£®3 Reduction of the System5£®2£®4 Strichartz Norms£¬ Fourier Restriction Norms and Related Estimates5£®3 Bilinear Estimates for Regular Interactions and Non-resonant Interactions5£®4 Energy Estimate on the Resonant Components5£®5 Convergence Results5£®5£®1 Limit Behavior of the Klein-Gordon-Zakharov System5£®5£®2 Uniform Bounds and Two Lemmas5£®6 Proof of the Main Results5£®7 Convergence in the Energy Space with Small Initial DataReferences