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Mathematics, Analysis of PDEs, math.AP
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.
