Blow-up for semilinear wave equations with initial data of slow decay in low space dimensions

We are concerned with the blow-up of classical solutions to the Cauchy problems for u = |u_t|^p in ℝⁿ X [0, ∞), 1 ≤ n ≤ 3. For this subject, the effect of the power p has been studied extensively, provided the initial data are compactly supported. However, the decay rate of the initial data also has an important role as well as the power p. Indeed, the slow decay of them causes blow-up in finite-time for any p > 1.