目录
 前辅文
 Introduction and summary
 I. An overview of results on the Cauchy problem for NLS
  1. Equations
  2. Wellposedness of the Cauchy problen
  3. Scattering results
  4. Estimates on the linear group
  5. Solving the Cauchy problem
  6. Derivative nonlinear Schrödinger equations
 II. Further comments
  1. Construction of blowup solutions for conformal NLS from the ground state
  2. Behaviour of higher Sobolev norms
  3. Fourier restriction theory beyond L2
  4. L2-concentration phenomenon
  5. The Schrödinger maximal function
  6. Derivative nonlinear Schrodinger equation
 III. 3D H1-critical defocusing NLS
  1. Consider 3D NLS
  2. Fix a time interval I=[0,T]
  3. Sketch of the argument
  4. A concentration property
  5. A version of Morawetz inequality
  6. Construction of an appropriate time interval
  7. Details on the perturbative analysis
  8. A variant of the method
 IV. Global wellposedness below energy norm
  1. Description of the method
  2. The example of the NLW
  3. The case of the nonlinear Schrödinger equation
  4. Symplectic capacities and symplectic Hilbert spaces
  5. Global wellposedness of the NLW (4.41)
 V. Nonlinear Schrödinger equation with periodic boundary conditions
  1. Introduction
  2. Results on the Cauchy problem
  3. Periodic Strichartz inequalities
  4. Sketch of proof of Theorems 2.1 and 2.7
  5. Invariant Gibbs measures (1D)
  6. Invarinat Gibbs measures (D>1)
  7. Invariant Gibbs measures (unbounded domains)
  8. Quasi-periodic solutions
 Appendix 1. Growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential
 Appendix 2. Zakharov systems
 References
 Index
 前辅文
 Introduction and summary
 I. An overview of results on the Cauchy problem for NLS
  1. Equations
  2. Wellposedness of the Cauchy problen
  3. Scattering results
  4. Estimates on the linear group
  5. Solving the Cauchy problem
  6. Derivative nonlinear Schrödinger equations
 II. Further comments
  1. Construction of blowup solutions for conformal NLS from the ground state
  2. Behaviour of higher Sobolev norms
  3. Fourier restriction theory beyond L2
  4. L2-concentration phenomenon
  5. The Schrödinger maximal function
  6. Derivative nonlinear Schrodinger equation
 III. 3D H1-critical defocusing NLS
  1. Consider 3D NLS
  2. Fix a time interval I=[0,T]
  3. Sketch of the argument
  4. A concentration property
  5. A version of Morawetz inequality
  6. Construction of an appropriate time interval
  7. Details on the perturbative analysis
  8. A variant of the method
 IV. Global wellposedness below energy norm
  1. Description of the method
  2. The example of the NLW
  3. The case of the nonlinear Schrödinger equation
  4. Symplectic capacities and symplectic Hilbert spaces
  5. Global wellposedness of the NLW (4.41)
 V. Nonlinear Schrödinger equation with periodic boundary conditions
  1. Introduction
  2. Results on the Cauchy problem
  3. Periodic Strichartz inequalities
  4. Sketch of proof of Theorems 2.1 and 2.7
  5. Invariant Gibbs measures (1D)
  6. Invarinat Gibbs measures (D>1)
  7. Invariant Gibbs measures (unbounded domains)
  8. Quasi-periodic solutions
 Appendix 1. Growth of Sobolev norms in linear Schrödinger equations with smooth time dependent potential
 Appendix 2. Zakharov systems
 References
 Index