Willmore Flow of Networks

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Julia Menzel
Abstract. We consider networks of curves in the plane moving according to the L^2-gradient flow of a variant of the elastic energy. In this talk we will prove short time existence in the case of networks composed by three curves that are required to meet in one or two triple junctions. As a variation of the result we additionally impose that they form an angle of 120 degrees at the triple junction(s). If time allows we will give some outlook on our expectations concerning the long time behaviour based on numerical work by John Barrett, Harald Garcke and Robert Nürnberg. The presented result is joint work with Harald Garcke and Alessandra Pluda.