Time decay for solutions to the Stokes equations with drift
  In this note, we study the behaviour of Lebesgue norms $\|v(\cdot,t)\|_p$ of solutions $v$ to the Cauchy problem for the Stokes system with drift $u$, which is supposed to be a divergence free smooth vector valued function satisfying a scale invariant condition. 
M. Schonbek, G. Seregin
math.AP