The Korteweg-de Vries Hierarchy in Rough Function Spaces
Explore a mathematical lecture on the Korteweg-de Vries (KdV) hierarchy in rough function spaces, delivered by Herbert Koch as part of the Thematic Programme on "Nonlinear Waves and Relativity" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the extension of Killip and Visan's wellposedness result for the KdV equation in H^{-1} to the full hierarchy. Discover the crucial role of the Miura map in translating the problem to the Gardner hierarchy in L2 and introducing a natural spectral parameter. Learn about the proof of existence and uniqueness of weak solutions to all equations of the Gardner hierarchy for initial data in L^2. Gain insights into this joint work with B. Liu and F. Klaus, which advances our understanding of nonlinear wave equations in mathematics and physics.