SHARP GLOBAL WELL-POSEDNESS OF THE BBM EQUATION IN LP TYPE SOBOLEV SPACES

The global well-posedness of the BBM equation is established in H-s,H-p(R) with s >= max {0,1/p - 1/2} and 1 <= p < infinity. Moreover, the well-posedness results are shown to be sharp in the sense that the solution map is no longer C-2 from H-s,H-p(R) to C([0,T]; H-s,H-p(R)) for smaller s or p. Finally, some growth bounds of global solutions in terms of time T are proved.