Geometric wave equations arise naturally in various branches of theoretical physics, e.g. as field equations in particle physics and general relativity or in the description of wave motion of surfaces immersed into a fixed target manifold. In this project, we focus on well-known model problems, in particular, on the wave maps equation and a higher order variant known as biharmonic wave maps. One of the central goals of this project concerns the investigation of the formation of singularities and the role of self-similar solutions in the blowup dynamics in the so-called energy supercritical case. Another aspect concerns the existence of global weak solutions for biharmonic wave maps for general target manifolds and the wellposedness of the Cauchy problem at low regularity.
DFG Programme
Collaborative Research Centres
