Global well-posedness for higher-order even nonlinearities

Establish a low-regularity global well-posedness theory for the generalised fractional BBM equation with higher-order even polynomial nonlinearities.

Background

The paper develops low-regularity global well-posedness results primarily for odd nonlinearities, using conservation of the Hamiltonian to control the L^{k+1} norm. For even k, the Hamiltonian does not provide the same control because the associated power term is not sign-definite. The author explicitly identifies the global theory for higher-order even powers as unresolved.