Remark on the global existence for the generalized Benjamin-Bona-Mahony equations in arbitrary dimension

In this paper, the global existence of the solutions to the initial boundary value problems of GBBM equations in arbitrary dimension d is further studied. It is proved that when the nonlinear function satisfies some polynomial-like growth bounds, there exists a unique global solution in the space C((O, ∞); W2,p(G) intersection W1,p(G)), with max(1,d/2) < p < ∞. (author). 6 refs