A uniqueness theorem for 3D semilinear wave equations satisfying the null condition

Abstract

In this paper, we prove a uniqueness theorem for a system of semilinear wave equations satisfying the null condition in ${\mathbb{R}}^{1+3}$. Suppose that two global solutions with $C_c^{\infty }$ initial data have equal initial data outside a ball and equal radiation fields outside a light cone. We show that these two solutions are equal either outside a hyperboloid or everywhere in the spacetime, depending on the sizes of the ball and the light cone.

43 pages, 1 figure. Revised based on a referee report

References in corpus (3)

• Uniqueness results for ill posed characteristic problems in curved space-times
• Decay estimates for nonradiative solutions of the energy-critical focusing wave equation
• Modified wave operators for a scalar quasilinear wave equation satisfying the weak null condition