Video library: S. B. Kuksin, KAM-theory for PDE with one and many space variables

VIDEO LIBRARY


International conference "Analysis and Singularities" dedicated to the 75th anniversary of Vladimir Igorevich Arnold December 17, 2012 15:40, Moscow, Dorodnitsyn Computing Center of the RAS (Vavilova, 40), 3rd floor

KAM-theory for PDE with one and many space variables S. B. Kuksin
Abstract: In late 1980's a version of the classical KAM-theory, applicable to hamiltonian PDE with one space variable, was developed. Recently this theory was extended to some space-multidimensional hamiltonian PDE. Namely, in [1-3] two different approaches to treat the multidimensional equations were suggested, which were later developed by a number of researches. In my talk I will discuss the space-multidimensional "KAM for PDE" theory and its differences with the one-dimensional case. Language: English References Bourgain J., “Quasi-periodic solutions of Hamiltonian perturbations of 2D linear Schrödinger equations”, Ann. of Math., 148 (1998), 363–439 Bourgain J., Green’s Function Estimates for Lattice Schrödinger Operators and Applications, Princeton University Press, 2004 Eliasson H., Kuksin S., “KAM for the nonlinear Schrödinger equation”, Ann. of Math., 172 (2010), 371–435