Global existence for nonlinear system of wave equations in 3-D domains
We study the initial-boundary problem for a nonlinear system of wave equations with Hamilton structure under Dirichlet's condition. We use the local-in-time Strichartz estimates from [Burq et al., J. Amer. Math. Soc. 21 (2008), 831–845], Morawetz–Pohožaev's identity derived in [Miao and Zhu, Nonlinear Anal. 67 (2007), 3136–3151], and an a priori estimate of the solutions restricted to the boundary to show the existence of global and unique solutions.