Global Mild Solutions for a Nonautonomous 2D Navier-Stokes Equations with Impulses at Variable Times

The present paper deals with existence and uniqueness of global mild solutions for a new model of Navier Stokes equations on R-2 subjected to impulse effects at variable times. By using the framework of impulsive/nonautonomous dynamical systems we are able to consider impulse effects in the system as well relax conditions on the external forcing term which is, in our case, non-linear and explicitly time-dependent, extending previous results on the specialized literature. Moreover, we also introduce sufficient conditions on the structure of the impulse set which ensure dissipativity for the system, i.e., uniform boundedness of global solutions starting in bounded sets, which is an indicative to the existence of objects as attractors.