Nonlinear Evolution Equations and Related Topics

March 10 (Tue)　14:30--15:30

Speaker

Herbert Koch　(Mathematical Institute of the University of Bonn)

Title

The Kadomtsev-Petviashvili II equation with two transversal directions

Abstract

　　The Kadomtsev-Petviashvili II equation describes interacting waves with weak transversal effects. Its study gives insights into such interactions in much broader situations.
　　In this joint work with J. Li we study global solutions for small initial data in a scaling invariant Sobolev space. Scattering is an immediate consequence.
　　A heuristic sketch using rough arguments shows that many of the interactions are simultaneously tight.
　　The actual proof relies on the adapted function spaces U^p and V^p, a fine Fourier decomposition, precise bilinear estimates, and good control of the high modulation part.