The Fractional Navier-Stokes Equations with delay conditions

Abstract

Throught this paper,we study the cauchy problem for the conformable fractional Navier-Stokes Equations (FNSE) with finite delay external forces, contains some hereditary features, on a bounded domain. We prove that there exist a unique local mild solutions for the initial datum, by using semigroup theory, conformable fractional calculus and Banach contraction theorem.With more conditions on delay external forces we establish the globality and continuation of the mild solutions.