It is well-known that there are global small data smooth solutions for the 3-D semilinear Klein–Gordon equations □u + u = F(u, ∂u) with cubic nonlinearities. However, for the short pulse initial data \((u,\partial_{t}u)(0,x)=(\delta^{\nu+1}u_{0}({x\over \delta}),\delta^{\nu}u_{1}({x\over \delta}))\) with ν ∈ ℝ and (u0, u1) ∈ C 0 ∞ (ℝ), which are a class of large initial data, we establish that when \(\nu\leq-{1\over 2}\) , the solution u can blow up in finite time for some suitable choices of (u0, u1) and cubic nonlinearity F(u, ∂u); when \(\nu >-{1\over 2}\) , the smooth solution u exists globally. Therefore, \(\nu=-{1\over 2}\) is just the critical power corresponding to the global existence or blowup of smooth short pulse solutions for the cubic semilinear Klein–Gordon equations.
