Abstract
Abstract
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.
Funder
Deutsche Forschungsgemeinschaft