A Regularity Criterion for the Navier-Stokes Equations in the Multiplier Spaces

Abstract EN

We exhibit a regularity condition concerning the pressure gradient for the Navier-Stokes equations in a special class.

It is shown that if the pressure gradient belongs to L2/(2−r)((0,T);ℳ(H˙r(ℝ3)→H˙−r(ℝ3))), where ℳ(H˙r(ℝ3)→H˙−r(ℝ3)) is the multipliers between Sobolev spaces whose definition is given later for 0