New Trends in Quantum and Classical Kinetic Equations and Related PDEs

Ill-posedness Results for Model Equations for Water Waves

Jerry Bona

University of Illinois-Chicago

The discussion will center around both deep and shallow water wave models. Certain naturally derived models are examined and shown to be ill-posed in Hadamard's classical sense. The ill-posedness does not stem from trying to work in very large function classes, but instead seems intrinsic to the models and obtains even in quite smooth function spaces.