Small solutions to nonlinear wave equations in the Sobolev spaces (Q2771479)

The authors prove the global well-posedness of the initial value problem in Sobolev spaces for the equation \(u_{tt}-\triangle u=f(u)\) and for small initial data, where \(u(t,x),f(u)\) are complex-valued functions, \(t\in [-T,T]\), \(x\in \mathbb{R}^{n}.\) The function \(f(u)\) behaves as a power ``\(u^{1+4/{n-1}}\)'' near zero and has arbitrary growth rate at infinity.