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简介
本书是一部分析学经典专著，以作者的最新研究为蓝本，证明基于两方面：基态的变分结构和这些态附近的非线性双曲动力学，这两方面的交互作用。本书适于为数学专业和物理专业的研究生和科研人员。书中详尽地呈现了三维中的Klein-Gordon三次方程，包括自由方程的Strichartz估计推导，和集中紧性争论导致的散射。 目次：基态能量以下的Klein-Gordon方程；基态能量Ⅰ之上，临近Q；基态能量Ⅱ之上，远离Q；基态能量Ⅲ之上：全局NLKG动力；该理论的更深研究。 读者对象：本书适用于偏微分方程和数学物理方向的研究生和科研人员。
目录
Introduction
2 The Klein—Gordon equation below the ground state energy
2.1 Basic existence theory
2.2 Stationary solutions， ground state
2.3 The Payne—Sattinger criterion， regions □S±
2.4 Scattering in □S+
2.5 Strichartz estimates for Klein—Gordon equations
2.6 Summary and conclusion
3 Above the ground state energy Ⅰ： Near Q
3.1 Energy landscape
3.2 Center， stable， and unstable manifolds in hyperbolic dynamics
3.3 Center—stable manifolds via the Lyapunov—Perron method
3.4 Dispersive estimates for the perturbed linear evolution
3.5 The center—stable manifold for the radial cubic NLS in R3
3.6 Summary and conclusion
4 Above the ground state energy Ⅱ： Moving away from Q
4.1 Nonlinear distance function， eigenmode dominance， ejection
4.2 J and Ko， K2 above the ground state energy
4.3 The one—pass theorem
4.4 Summary and conclusion
5 Above the ground state energy Ⅲ： Global NLKG dynamics
5.1 Statement of the main results on global dynamics
5.2 The blowup／scattering dichotomy in the ejection case
5.3 Proofs of the main results
5.4 Summary and conclusion
6 Further developments of the theory
6.1 The nonradial cubic NLKG equation in R3
6.2 The one—dimensional NLKG equation
6.3 The cubic radial NLS equation in R3
6.4 The energy criticalwave equation
References
Index
2 The Klein—Gordon equation below the ground state energy
2.1 Basic existence theory
2.2 Stationary solutions， ground state
2.3 The Payne—Sattinger criterion， regions □S±
2.4 Scattering in □S+
2.5 Strichartz estimates for Klein—Gordon equations
2.6 Summary and conclusion
3 Above the ground state energy Ⅰ： Near Q
3.1 Energy landscape
3.2 Center， stable， and unstable manifolds in hyperbolic dynamics
3.3 Center—stable manifolds via the Lyapunov—Perron method
3.4 Dispersive estimates for the perturbed linear evolution
3.5 The center—stable manifold for the radial cubic NLS in R3
3.6 Summary and conclusion
4 Above the ground state energy Ⅱ： Moving away from Q
4.1 Nonlinear distance function， eigenmode dominance， ejection
4.2 J and Ko， K2 above the ground state energy
4.3 The one—pass theorem
4.4 Summary and conclusion
5 Above the ground state energy Ⅲ： Global NLKG dynamics
5.1 Statement of the main results on global dynamics
5.2 The blowup／scattering dichotomy in the ejection case
5.3 Proofs of the main results
5.4 Summary and conclusion
6 Further developments of the theory
6.1 The nonradial cubic NLKG equation in R3
6.2 The one—dimensional NLKG equation
6.3 The cubic radial NLS equation in R3
6.4 The energy criticalwave equation
References
Index
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