Related papers: Computability of the Solutions to Navier-Stokes Eq…
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,…
We are concerned with the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Navier-Stokes equations with vacuum as far-field density. It is proved that if the initial density decays not too slow at infinity, the 2D…
In this paper, we rigorously derive the compressible one-fluid Navier-Stokes equation from the scaled compressible two-fluid Navier-Stokes-Maxwell equations locally in time under the assumption that the initial data are well prepared. We…
In this master thesis we have compared different second order stabilized explicit Runge-Kutta methods when applied to the incompressible Navier-Stokes equations by means of a projection method and a differential algebraic approach. We…
We consider the equations of Navier-Stokes modeling viscous fluid flow past a moving or rotating obstacle in $\mathbb{R}^d$ subject to a prescribed velocity condition at infinity. In contrast to previously known results, where the…
We study properties of the solutions to Navier-Stokes system on compact Riemannian manifolds. The motivation for such a formulation comes from atmospheric models as well as some thin film flows on curved surfaces. There are different…
We investigate existence, Liouville type theorems and regularity results for the 3D stationary and incompressible fractional Navier-Stokes equations: in this setting the usual Laplacian is replaced by its fractional power…
In this paper we analyze the theoretical properties of a stochastic representation of the incompressible Navier-Stokes equations defined in the framework of the modeling under location uncertainty (LU). This setup built from a stochastic…
We establish a Liouville theorem for bounded mild ancient solutions to the axi-symmetric incompressible Navier-Stokes equations on $(-\infty, 0] \times (\mathbb{R}^2 \times \mathbb{T}^1)$. This is a step forward to completely solve the…
In this paper we establish a sharp non-uniqueness result for stochastic $d$-dimensional ($d\geq2$) incompressible Navier-Stokes equations. First, for every divergence free initial condition in $L^2$ we show existence of infinite many global…
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…
This note echoes the talk given by the second author during the Journ\'ees EDP 2018 in Obernai. Its aim is to provide an overview and a sketch of proof of the result obtained by the authors, concerning the controllability of the…
In this article, we devote to the existence of an $N$-dimensional inertial manifold for the incompressible Navier-Stokes equations in $\mathbb{T}^{d}$ ($d=2,3$). Our results can be summarized as two aspects: Firstly, we construct an…
The work described here shows that the known variational principle for the Navier-Stokes equations and the adjoint system can be modified to produce a set of Euler-Lagrange variational equations which have the same order and same solution…
We study the immersed boundary problem in 2-D. It models a 1-D elastic closed string immersed and moving in a fluid that fills the entire plane, where the fluid motion is governed by the 2-D incompressible Navier-Stokes equation with a…
We prove the analyticity in time for solutions of two parabolic equations in the whole space, without any decaying or vanishing conditions. One of them involves solutions to the heat equation of exponential growth of order $2$ on $\M$. Here…
Solutions of the Navier-Stokes and Euler equations with initial conditions for 2D and 3D cases were obtained in the form of converging series, by an analytical iterative method using Fourier and Laplace transforms \cite{TT10,TT11}. There…
The energy equalities of compressible Navier-Stokes equations with general pressure law and degenerate viscosities are studied. By using a unified approach, we give sufficient conditions on the regularity of weak solutions for these…
We consider the Cauchy problem for the incompressible Navier--Stokes equations on the whole space $\mathbb{R}^3$, with initial value $\vec u_0\in {\rm BMO}^{-1}$ (as in Koch and Tataru's theorem) and with force $\vec f=\Div \mathbb{F}$…
In this paper, we deal with the convergence of an iterative scheme for the 2-D stochastic Navier-Stokes Equations on the torus suggested by the Lie-Trotter product formulas for stochastic differential equations of parabolic type. The…