Existence of solutions for a class of Navier–Stokes equations with infinite delay

Abstract

In this paper, a class of Navier–Stokes equations with infinite delay is considered. It includes delays in the convective and the forcing terms. We discuss the existence of mild and classical solutions for the problem. We establish the results for an abstract delay problem by using the fact that the Stokes operator is the infinitesimal generator of an analytic semigroup of bounded linear operators. Finally, we apply these abstract results to our particular situation.

Keywords:

• Navier–Stokes equations
• infinite delays
• mild solution

AMS Subject Classifications:

• 35R10
• 35Q30
• 47D05

Acknowledgments

We would like to thank E. Hernández for interesting discussions about this subject.

Additional information

Funding

S.M. Guzzo was partially supported by PICDT/Capes – Brazil. G. Planas has been partially supported by CNPq – Brazil, [grant number 302865/2012-8].