Abstract
In this paper we consider the Cauchy problem for the stochastic modified Kawahara equation, which is a fifth-order shallow water wave equation. We prove local well-posedness for data in
H
s
(
R
)
,
s
≥
−
1
/
4
. Moreover, we get the global existence for
L
2
(
R
)
solutions. Due to the non-zero singularity of the phase function, a fixed point argument and the Fourier restriction method are proposed.