Related papers: The second iterate for the Navier-Stokes equation
A model is developed describing the approach to a finite-time singularity of the Navier-Stokes equations for two interacting vortices. The model is derived from a combination of the Biot-Savart law and an equation describing the evolution…
A mathematical model describing the flow of two-phase fluids in a bounded container $\Omega$ is considered under the assumption that the phase transition process is influenced by inertial effects. The model couples a variant of the…
The paper is concerned with the existence and uniqueness of a strong solution to a two-dimensional backward stochastic Navier-Stokes equation with nonlinear forcing, driven by a Brownian motion. We use the spectral approximation and the…
A three-dimensional chemotaxis-Navier-Stokes system is considered. It is known that for all suitably regular initial data, a corresponding initial-boundary value problem admits at least one global weak solution which can be obtained as the…
We study 2D Navier-Stokes equations with a constraint on $L^2$ energy of the solution. We prove the existence and uniqueness of a global solution for the constrained Navier-Stokes equation on $\R^2$ and $\T$, by a fixed point argument. We…
We propose an efficient, accurate and robust implicit solver for the incompressible Navier-Stokes equations, based on a DG spatial discretization and on the TR-BDF2 method for time discretization. The effectiveness of the method is…
Exponential stabilization to time-dependent trajectories for the incompressible Navier-Stokes equations is achieved with explicit feedback controls. The fluid is contained in two-dimensional spatial domains and the control force is, at each…
The Navier--Stokes equations for incompressible flows past a two--dimensional sphere are considered in this article. The existence of an inertial form of the equations is established. Furthermore for the first time for fluid equations, we…
We study in this article the solutions of the Navier-Stokes equations, with initial data in the closure of the Schwartz class in BMO-1. For such intial data, we obtain the existence and uniqueness of a global solution, and an estimate on…
We survey the various constructions of forward self-similar solutions (and generalizations of self-similar solutions) to the Navier-Stokes equations. We also include and prove an extension of a recent result from [7].
We consider an initial-boundary value problem for the chemotaxis-Navier--Stokes system \begin{align*} \left\{ \begin{array}{c@{\quad}l@{\quad}l@{\,}c} n_{t}+u\cdot\nabla n=\nabla\cdot\big(D(n)\nabla n-nS(x,n,c)\cdot\nabla c\big),\…
This paper presents a unique continuation estimate for 2-D Stokes equations with the Naiver slip boundary condition in a bounded and simply connected domain. Consequently, an observability estimate for this equation from a subset of…
We study the boundary value problem for the stationary Navier--Stokes system in two dimensional exterior domain. We prove that any solution of this problem with finite Dirichlet integral is uniformly bounded. Also we prove the existence…
Introduction: the Navier-Stokes equations are essential in fluid dynamics, describing the motion of fluids like liquids and gases. Solving these equations, especially in complex flows and high-Reynolds-number regimes, is a significant…
The first goal of this paper is to study the large time behavior of solutions to the Cauchy problem for the 3-dimensional incompressible Navier-Stokes system. The Marcinkiewicz space $L^{3,\infty}$ is used to prove some asymptotic stability…
We study the inviscid limit problem for the incompressible Navier-Stokes equation on a half-plane with a Navier boundary condition depending on the viscosity. On one hand, we prove the $L^2$ convergence of Leray solutions to the solution of…
We introduce corrections to the Navier-Stokes equation arising from the transitions between molecular states and the injection of external energy. In the simplest application of the proposed post Navier-Stokes equation, we find a…
In this paper, the strong formulation of the generalised Navier-Stokes momentum equation is investigated. Specifically, the formulation of shear-stress divergence is investigated, due to its effect on the performance and accuracy of…
A modified version of the three dimensional Navier-Stokes equations is considered with periodic boundary conditions. A bounded constant delay is introduced into the convective term, that produces a regularizing effect on the solution. In…
A new iterative projection method is proposed to solve the unsteady Navier-Stokes equations with high Reynolds numbers. The convectional projection method attempts to project the intermediate velocity to the divergence free space only once…