(12018)A LARGE DATA REGIME FOR NON-LINEAR WAVE EQUATIONS

来源:数学科学研究中心

Abstract. For semi-linear wave equations with null form non-linearities on R3+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 speci c incoming null geodesic in such a way that almost all of the energy is con ned in a tubular neighborhood of the geodesic and almost no energy radiating out of this tubular neighborhood.

  • A LARGE DATA REGIME FOR NON-LINEAR WAVE EQUATIONS.pdf