Wave maps on a wormhole

We consider equivariant wave maps from a wormhole spacetime into the three-sphere. This toy-model is designed for gaining insight into the dissipation-by-dispersion phenomena, in particular the soliton resolution conjecture. We first prove that for each topological degree of the map there exists a unique static solution (harmonic map) which is linearly stable. Then, using the hyperboloidal formulation of the initial value problem, we give numerical evidence that every solution starting from smooth initial data of any topological degree evolves asymptotically to the harmonic map of the same degree. The late-time asymptotics of this relaxation process is described in detail.