Global existence for nonlinear elastic waves in high space dimensions

In Georgiev et al. (2005), the authors proved the global existence of solutions to the Cauchy problem of nonlinear elastic waves with memory for space dimensions n≥3. In this manuscript, we show that in high space dimensions n≥4, even without such memory effect, global solutions can be also constructed. The main tool we used is the vector fields method adapted to elastic waves in Sideris's work (Sideris, 2000).