Well-posedness of the periodic dispersion-generalized Benjamin–Ono equation in the weakly dispersive regime

We study the dispersion-generalized Benjamin–Ono equation in the periodic setting. This equation interpolates between the Benjamin–Ono equation ( α = 1 ) and the inviscid Burgers’ equation ( α = 0 ). We obtain local well-posedness in H s ( T ) for s > 3 2 − α and α ∈ ( 0 , 1 ) by using the short-time Fourier restriction method.