Sharp global well-posedness of the BBM equation in Lᵖ type Sobolev spaces

The global well-posedness of the BBM equation is established in Hs,p(R) with s≥ max\0,1/p-1/2\ and 1≤ p<∞. Moreover, the well-posedness results are shown to be sharp in the sense that the solution map is no longer C² from Hs,p(R) to C([0,T];Hs,p(R)) for smaller s or p. Finally, some growth bounds of global solutions in terms of time T are proved.