Spectral theory and nonlinear partial differential equations: A survey

By Wilhelm Schlag. 2006

56 citations recorded by the source corpus.

This paper reviews some of the recent work of the author on stable manifolds for unstable evolution equations. In particular, we discuss such a result, jointly with Joachim Krieger, for the critical focusing nonlinear wave equation in three dimensions.

Subfields: Control and Systems Engineering, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/44bf8728b33ebf1446c4c1c6e8662f15ac34cad4

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Raphael Cote
2. Yvan Martel
3. F. Merle
4. Thomas Duyckaerts
5. Marina Chugunova
6. Dmitry E. Pelinovsky
7. Pierre Raphael
8. Hatem Zaag

In Mathematical Physics

1. Raphael Cote
2. F. Merle
3. Yvan Martel
4. Thomas Duyckaerts
5. Pierre Raphael
6. Carlos E. Kenig
7. Hatem Zaag
8. Vianney Combet

In Numerical Analysis

1. Yvan Martel
2. F. Merle
3. Raphael Cote
4. Marina Chugunova
5. Dmitry E. Pelinovsky
6. Thomas Duyckaerts

Citations in the corpus

• Dynamic of Threshold Solutions for Energy-Critical NlS (2007, result): “1, which is a variation of the classical proof (see [Gri90] and the survey [Sch06] for similar results).”
• Construction of multi-soliton solutions for the $L^2$-supercritical gKdV and NLS equations (2009, methodology): “[28] Wilhelm Schlag, Spectral theory and nonlinear partial differential equations: a survey, Discrete Contin.”
• Count of eigenvalues in the generalized eigenvalue problem (2006, background): “growing sequence of publications about characterization of unstable eigenvalues of this generalized eigenvalue problem in terms of isolated eigenvalues of the operatorsA andK 1 [CPV05, GKP04, KKS04, KP05, P05, S06 ].”