Global mild solutions for the nonautonomous 2D Navier-Stokes equations with impulse effects

TL;DR

This paper establishes the existence, uniqueness, and dissipativity of global mild solutions for the nonautonomous 2D Navier-Stokes equations with impulse effects, extending previous results to include explicit time dependence.

Contribution

It introduces a framework for analyzing nonautonomous Navier-Stokes equations with impulses, allowing explicit time-dependent nonlinear terms and providing conditions for solution boundedness.

Findings

Proved existence and uniqueness of solutions.

Established dissipativity conditions.

Extended previous models to include time-dependent nonlinearities.

Abstract

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.