Abstract
In this paper we consider the regularity criteria for weak solutions to the 3D MHD equations. It is proved that under the condition
b
being in the Serrin's regularity class, if the pressure
p
belongs to
L
α
,
γ
with
2
α
+
3
γ
⩽
2
or the gradient field of pressure
∇
p
belongs to
L
α
,
γ
with
2
α
+
3
γ
⩽
3
on
[
0
,
T
]
, then the solution remains smooth on
[
0
,
T
]
.