What liquid? What applied pressure?
"magnetic field that is applicable to liquid" -- What does that mean?
"The density of liquid will be deferent according to position ,and the heavier will go down ,the lighter will move up in a non-uniform magnetic field" -- Whatever are you talking about?
"If the magnetic field keep non-uniform ,the convection current will be not stop for ever." -- Only if there is no friction, that is the liquid is superfluid helium. Otherwise, viscose friction will stop the motion.