On Some Classes of Time-Periodic Solutions for the Navier-Stokes Equations in the Whole Space

Existence of Time-periodic Solutions to Incompressible Navier-stokes Equations in the Whole Space

In this article, we assume that the force field acting over a fluid is periodic on time and the velocity of the liquid is zero at spatial infinity. We prove the existence of time-periodic solutions to the system governing the motion of an incompressible fluid filling the whole space.

Solutions to Three-dimensional Navier-stokes Equations for Incompressible Fluids

This article gives explicit solutions to the space-periodic NavierStokes problem with non-periodic pressure. These type of solutions are not unique and by using such solutions one can construct a periodic, smooth, divergence-free initial vector field allowing a space-periodic and time-bounded external force such that there exists a smooth solution to the 3-dimensional Navier-Stokes equations fo...

A comparative study between two numerical solutions of the Navier-Stokes equations

The present study aimed to investigate two numerical solutions of the Navier-Stokes equations. For this purpose, the mentioned flow equations were written in two different formulations, namely (i) velocity-pressure and (ii) vorticity-stream function formulations. Solution algorithms and boundary conditions were presented for both formulations and the efficiency of each formulation was investiga...

Time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space with a drift term: Asymptotic profile at spatial infinity

Sufficient Conditions for the Regularity to the 3d Navier–stokes Equations

In this paper we consider the three–dimensional Navier–Stokes equations subject to periodic boundary conditions or in the whole space. We provide sufficient conditions, in terms of one direction derivative of the velocity field, namely, uz , for the regularity of strong solutions to the three-dimensional Navier–Stokes equations.