A large data regime for nonlinear wave equations

  • Jinhua Wang

    Max-Planck-Institute for Gravitational Physics, Golm, Germany
  • Pin Yu

    Tsinghua University, Beijing, China


For semi-linear wave equations with null form nonlinearities on R3+1\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 speci fic incoming null geodesic in such a way that almost all of the energy is concentrated in a tubular neighborhood of the geodesic and almost no energy radiates out of this neighborhood.

Cite this article

Jinhua Wang, Pin Yu, A large data regime for nonlinear wave equations. J. Eur. Math. Soc. 18 (2016), no. 3, pp. 575–622

DOI 10.4171/JEMS/597