Global mild solutions for the nonautonomous 2D Navier-Stokes equations   with impulse effects
  The present paper deals with existence and uniqueness of global mild solutions for the 2D Navier-Stokes equations with impulses. Using the framework of nonautonomous dynamical systems, we extend previous results considering the 2D Navier-Stokes equations with impulse effects and allowing that the nonlinear terms are explicitly time-dependent. Additionally, we present sufficient conditions to obtain dissipativity (boundedness) for solutions starting in bounded sets. 
Everaldo M. Bonotto, Jaqueline G. Mesquita, Ricardo P. Silva
math.AP