Global existence of smooth solution to relativistic membrane equation with large data

This paper is concerned with the Cauchy problem for relativistic membrane equation (RME) embedded in $${\mathbb {R}}^{1+(1+n)}$$ $$n=2, \, 3$$ . We show that RME a class of large (in energy norm) initial data admits global, smooth solution. The are given by short pulse type, which introduced Christodoulou his work on formation black holes [10]. Due to quasilinear feature RME, we construct two multipliers adapted geometry and present an efficient way proving global existence solution geometric wave double null structure. also derive asymptotic future infinity find out nonlinear (expanding) effect at infinity.