不变流形和色散型哈密顿发展方程 英文PDF电子书下载

1 Introduction 1

2 The Klein-Gordon equation below the ground state energy 17

2.1 Basic existence theory 20

2.2 Stationary solutions,ground state 29

2.3 The Payne-Sattinger criterion,regions ？ 34

2.4 Scattering in ？ 37

2.5 Strichartz estimates for Klein-Gordon equations 63

2.6 Summary and conclusion 77

3 Above the ground state energy Ⅰ:Near Q 79

3.1 Energy landscape 80

3.2 Center,stable,and unstable manifolds in hyperbolic dynamics 85

3.3 Center-stable manifolds via the Lyapunov-Perron method 108

3.4 Dispersive estimates for the perturbed linear evolution 117

3.5 The center-stable manifold for the radial cubic NLS in R3 130

3.6 Summary and conclusion 143

4 Above the ground state energy Ⅱ:Moving away from Q 145

4.1 Nonlinear distance function,eigenmode dominance,ejection 145

4.2 J and K0,K2 above the ground state energy 158

4.3 The one-pass theorem 162

4.4 Summary and conclusion 170

5 Above the ground state energy Ⅲ:Global NLKG dynamics 173

5.1 Statement of the main results on global dynamics 174

5.2 The blowup/scattering dichotomy in the ejection case 177

5.3 Proofs of the main results 182

5.4 Summary and conclusion 188

6 Further developments of the theory 191

6.1 The nonradial cubic NLKG equation in R3 194

6.2 The one-dimensional NLKG equation 204

6.3 The cubic radial NLS equation in R3 218

6.4 The energy critical wave equation 232

References 241

Index 251