Spectral theory and nonlinear partial differential equations: a survey (Q874381)

The paper reviews some of the recent work of the author and J. Krieger on stable manifolds for unstable evolution equations. More specifically, the author gives some ideas of how to prove a recent result by Krieger and the author for the quintic wave equation \[ \square \psi-\psi^5=0 \quad\text{ in }\mathbb R^3 \] This is the focusing, \(H^1\)-critical nonlinear wave equation. Much attention has been given to the defocusing equation \[ \square \psi+\psi^5=0 \quad\text{ in }\mathbb R^3. \]