A study of the time fractional Navier-Stokes equations for vertical flow

Abstract

Navier-Stokes (NS) equations dealing with gravitational force with time-fractional derivatives are discussed in this paper. These equations can be used to predict fluid velocity and pressure for a given geometry. This paper investigates the local and global existence and uniqueness of mild solutions to NS equations for the time fractional differential operator. We also work on the regularity effects of such types of equations were caused by orthogonal flow.

Keywords

• navier-stokes equations
• mild solution
• existence and uniqueness
• caputo fractional derivative
• mittag-leffler functions
• regularity