In this paper, we study well-posedness and the global solutions to the higher-order Camassa-Holm equations with fractional inertia operator in Besov space. When a∈[21,1), we prove the existence of the solutions in space Bp,1s(R)
Nearby in the stack
with
s≥1+p1
and
p<a−211
, the existence and uniqueness of the solutions in space
Bp,1s(R)
with
s≥1+2a−min{p1,p′1},
and the local well-posedness in space
Bp,1s(R)
with
s>1+2a−min{p1,p′1}
. When
a>1,
we obtain the existence of the solutions in space
Bp,1s(R)
with
s≥a+max{p1,21}
and the local well-posedness in space
Bp,1s(R)
with
s≥1+a+max{p1,21}
. Moreover, we obtain two results about the global solutions.