A NOTE ON “THE CAUCHY PROBLEM FOR COUPLED IMBQ EQUATIONS”

In this article, we prove that the Cauchy problem for a N-dimensional system of nonlinear wave equations utt-aΔutt=Δf(u,v),    x ∈ ℝN, t > 0,utt-aΔutt=Δg(u,v),    x ∈ ℝN, t > 0admits a unique global generalized solution in C3([0,∞);Wm,p(ℝN)∩ L∞(ℝN) ∩ L2(ℝN)) (m≥ 0 is an integer, 1≤ p ≤ ∞) and a unique global classical solution in C3([0,∞);Wm,p∩ L∞ ∩ L2)  (m > 2+ NP), the sufficient conditions of the blow up of the solution in finite time are given, and also two examples are given.