Related papers: The second iterate for the Navier-Stokes equation
Navier-Stokes equations are investigated in a functional setting in 3D open sets, bounded or not, without assuming any regularity of the boundary. The main idea is to find a correct definition of the Stokes operator in a suitable Hilbert…
We consider an iterative resolution scheme for a broad class of active scalar equations with a fractional power \gamma of the Laplacian and focus our attention on the second iterate. The main objective of our work is to analyze boundedness…
It is well known that the choice of the iterative method is crucial in determining the speed of the converged solution. This article presents a detailed comparison between several iterative techniques for solving incmopressible…
Solution of the Navier-Stokes equations with initial conditions (Cauchy problem) for 2D and 3D cases was obtained in the convergence series form by iterative method using Fourier and Laplace transforms in paper $\cite{TT02}$. For several…
We introduce a modified version of the two-dimensional Navier-Stokes equation, preserving energy and momentum of inertia, which is motivated by the occurrence of different dissipation time scales and related to the gradient flow structure…
We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…
The 3D spatially periodic Navier-Stokes equation is posed as a nonlinear matrix differential equation. When the flow is assumed to be a time series having unknown wavenumber coefficients, then the matrix in this periodic Navier-Stokes…
We consider the incompressible and stationary Stokes equations on an infinite two-dimensional wedge with non-scaling invariant Navier-slip boundary conditions. We prove well-posedness and higher regularity of the Stokes problem in a certain…
An algorithm for generating a class of closed form solutions to the Navier-Stokes equations is suggested, with examples. Of particular interest are those exact solutions that exhibit intermittency, tertiary Hopf bifurcations, flow reversal,…
In this paper, we utilize some series and an iterative method to solve some Navier-Stokes equations with the initial conditions being some complex-valued periodic functions on $R^3$. Then a new strategy for dealing with the conjecture of…
In this paper we will shows the solutions of Navier-Stokes with Oseen theory. The composition of turbulent solutions is a sum of regular solutions in a bounded space. We will show an another demonstration of solutions for Navier-Stokes…
In this paper, we study the initial and boundary value problem of the Navier-Stokes equations in the half space. We prove the unique existence of weak solution $u\in L^q(\R_+\times (0,T))$ with $\nabla u\in L^{\frac{q}{2}}_{loc}(\R_+\times…
The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time.…
In this paper, we consider the solvability of the two-dimensional stationary Navier--Stokes equations on the whole plane $\mathbb{R}^2$. In [6], it was proved that the stationary Navier--Stokes equations on $\mathbb{R}^2$ is ill-posed for…
In this paper, we study the long-time behavior of solutions to the two-dimensional Navier-Stokes equations in the presence of Couette flow on the half plane with Navier-slip boundary conditions. We prove that the total vorticity will…
We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of…
This article studies the uniqueness of the weak solution of the incompressible Navier-Stokes Equations in the 3-dimensional case. Here, the investigation is provided using two different approaches. The first (the main) result is obtained…
In this paper we consider the system of the non-steady Navier-Stokes equations with mixed boundary conditions. We study the existence and uniqueness of a solution of this system. We define Banach spaces $X$ and $Y$, respectively, to be the…
We develop a novel and efficient iterative scheme for solving incompressible steady Navier-Stokes equations. The method is an adaptation of the Incremental Viscosity Splitting approximation for unsteady flows to steady equations. At each…
We analyze and test a simple-to-implement two-step iteration for the incompressible Navier-Stokes equations that consists of first applying the Picard iteration and then applying the Newton iteration to the Picard output. We prove that this…