Extended lifespan of the fractional BBM equation

For 0 < α 1, N ⩾ 2 and with initial data ‖ u H + = ε, sufficiently small, we show that the existence time for solutions of fractional BBM equation ∂ t x | D 0, can be extended from hyperbolic 1 ε to . proof use a quasilinear modified energy method, based on normal form transformation as in Hunter, Ifrim, Tataru, Wong (Proc. Am. Math. Soc., 143(8) (2015) 3407–3412).