Global existence for nonlinear system of wave equations in 3-D domains
Volume 38 / 2011
Applicationes Mathematicae 38 (2011), 435-452
MSC: 35L05, 35L70.
DOI: 10.4064/am38-4-3
Abstract
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.
