Global solutions of nonlinear wave equations with large energy

Abstract

In this paper, we give a criterion on the Cauchy data for the semilinear wave equations satisfying the null condition in ${\mathbb{R}}^{+}\times {\mathbb{R}}^3$ such that the energy of the data can be arbitrarily large while the solution is still globally in time in the future.

16pages

References in corpus (4)

• On the quasilinear wave equations in time dependent inhomogeneous media
• Global regularity of wave maps VII. Control of delocalised or dispersed solutions
• Dynamical formation of black holes due to the condensation of matter field
• A Large Data Regime for non-linear Wave Equations

Cited by in corpus (3)

• On the quasilinear wave equations in time dependent inhomogeneous media
• On classical global solutions of nonlinear wave equations with large data
• Nonlinear Wave Equations With Null Condition On Extremal Reissner-Nordström Spacetimes I: Spherical Symmetry