Jia-Yuan Dai (Freie Universität Berlin)
Tuesday, January 16, 2018 - 15:15
Arnimallee 7, 14195 Berlin-Dahlem, Seminarraum 140
We consider a class of Gowdy spacetimes that reduces the Einstein’s field equation to a system of two semilinear wave equations, by assuming a universe without matter, in which the gravitational wave fronts repeat in space and are mutually parallel. To prove the existence of local solutions of the system, we add a linear perturbation and seek periodic-in-space solutions. The idea of the proof is to apply the Lyapunov-Schmidt reduction. We will solve a related small-divisor problem and discuss how to design the correct functional setting that fits to the nonlinearity. This ongoing research is a joint work with Dr. Hannes Stuke.
submitted by Ulrike Geiger (ulrike.geiger@fu-berlin.de, (030)838-75406)