Tuesday, June 4, 2024 - 14:30 in ZiF
Wave maps in dimension 1+1 with an external forcing
A talk in the Harmonic and Stochastic Analysis of Dispersive PDEs series by
Zdzislaw Brzeniak from University of York
| Abstract: |
I will talk about the local and global well-posedness theory in L1, inspired by the approach
of Keel and Tao from 1998 paper "Local and global well-posedness of wave maps on R1+1 for
rough data", for the forced wave map equation in the “external” formalism. In this context,
the target manifold is treated as a submanifold of a Euclidean space. As a byproduct, we can
reprove Y. Zhou’s uniqueness result from 1999 paper "Uniqueness of weak solutions of 1+1
dimensional wave maps", leading to the uniqueness of weak solutions with locally finite energy.
Additionally, we achieve the scattering of such solutions through a conformal compactification
argument. This talk is based on a joint paper with Jacek Jendrej (Paris) and Nimit Rana
(York) of the same title, arXiv:2404.09195.
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