Diff. Geom, Math. Phys., PDE Seminar: Emil Wiedemann

Since the famous work of V. Scheffer about 20 years ago, it has been known that the Cauchy problem for the incompressible Euler equations has non-unique weak solutions. Recently, De Lellis and Szekelyhidi demonstrated that this phenomenon can be viewed as an instance of the so-called h-principle, thereby providing a shorter and more general proof of the non-uniqueness. In this talk I will briefly review their method and then present some subsequent results, including global existence and non-uniqueness for 3D Euler, the approximation of measure-valued solutions by weak ones, and non-uniqueness for shear flow initial data.