Notes on Boussinesq Equation

Contents
Preface
v
Chapter 1. Introduction 1
Chapter 2. Linear Problem 11
2.1. L p –L q estimates 11
2.2. Local Smoothing Effects 19
2.3. Further Linear Estimates 21
Chapter 3. Nonlinear Problem. Local Theory 25
3.1. Local Existence Theory in L 2 25
3.2. Local Existence Theory in H 1 29
3.3. Critical case in L 2 35
Chapter 4. Global Theory. Persistence 39
4.1. Global Theory in H 1 39
4.2. Persistence 40
Chapter 5. Asymptotic Behavior of Solutions 43
5.1. Decay 43
5.2. Nonlinear Scattering 45
5.3. Blow-up 50
Appendix A. 57
A.1. Fourier Transform 57
A.2. Interpolation of Operators 59
A.3. Fractional Integral Theorem 60
A.4. Sobolev Spaces 61
Bibliography 63
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