The Navier-Stokes flow with linearly growing initial velocity in the whole space

Axisymmetric Flow of Navier-stokes Fluid in the Whole Space with Non-zero Angular Velocity Component

We study axisymmetric solutions to the Navier-Stokes equations in the whole three-dimensional space. We find conditions on the radial and angular components of the velocity field which are sufficient for proving the regularity of weak solutions.

Investigation of instable fluid velocity in pipes with internal nanofluid flow based on Navier-Stokes equations

In this article, the instable fluid velocity in the pipes with internal nanofluid is studied. The fluid is mixed by SiO2, AL2O3, CuO and TiO2 nanoparticles in which the equivalent characteristic of nanofluid is calculated by rule of mixture. The force induced by the nanofluid is assumed in radial direction and is obtained by Navier-Stokes equation considering viscosity of nanofluid. The displac...

Existence of Navier-stokes Flow in the Half Space with Non-decaying Initial Data

L2(Rn) estimate of the solution to the Navier-Stokes equations with linearly growth initial data

In this article, we consider the incompressible Navier-Stokes equations with linearly growing initial data U0 := u0(x) −Mx. Here M is an n × n matrix, trM = 0, M2 is symmetric and u0 ∈ L2(Rn) ∩ Ln(Rn). Under these conditions, we consider v(t) := u(t) − eu0, where u(x) := U(x) −Mx and U(x) is the mild solution of the incompressible Navier-Stokes equations with linearly growing initial data. We s...

Optimization with the time-dependent Navier-Stokes equations as constraints

In this paper, optimal distributed control of the time-dependent Navier-Stokes equations is considered. The control problem involves the minimization of a measure of the distance between the velocity field and a given target velocity field. A mixed numerical method involving a quasi-Newton algorithm, a novel calculation of the gradients and an inhomogeneous Navier-Stokes solver, to find the opt...