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Journal Article

A Large Data Regime for non-linear Wave Equations

MPS-Authors

Wang,  Jinhua
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1210.2056.pdf
(Preprint), 707KB

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Citation

Wang, J., & Yu, P. (2016). A Large Data Regime for non-linear Wave Equations. Journal of the European Mathematical Society, 18(3), 575-622. doi:10.4171/JEMS/597.


Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-7184-2
Abstract
For semi-linear wave equations with null form non-linearities on $\mathbb{R}^{3+1}$, we exhibit an open set of initial data which are allowed to be large in energy spaces, yet we can still obtain global solutions in the future. We also exhibit a set of localized data for which the corresponding solutions are strongly focused, which in geometric terms means that a wave travels along an specific incoming null geodesic in such a way that almost all of the energy is confined in a tubular neighborhood of the geodesic and almost no energy radiating out of this tubular neighborhood.