Related papers: Regularity Criterion for Solutions of Three-Dimens…
We investigate the nonlinear instability of a smooth steady density profile solution of the threedimensional nonhomogeneous incompressible Navier-Stokes equations in the presence of a uniform gravitational field, including a Rayleigh-Taylor…
The purpose of this article is to establish bounds from below for the life span of regular solutions to the incompressible Navier-Stokes system, whichinvolve norms not only of the initial data, but also of nonlinear functions of the initial…
This paper is concerned with a 2D channel flow that is periodic horizontally but bounded above and below by hard walls. We assume the presence of horizontal viscosity only. We study the well-posedness, large-time behavior, and stability of…
We study the existence of regular solutions of the incompressible stationary Navier-Stokes equations in $n$-dimensional Euclidean space with a given bounded external force of compact support. In dimensions $n\le 5$, the existence of such…
It is shown both locally and globally that $L_t^{\infty}(L_x^{3,q})$ solutions to the three-dimensional Navier-Stokes equations are regular provided $q\not=\infty$. Here $L_x^{3,q}$, $0<q\leq\infty$, is an increasing scale of Lorentz spaces…
Consider an axis-symmetric suitable weak solution of 3D incompressible Navier-Stokes equation with nontrivial swirl. If the solution satisfies a slightly supercritical assumption, we will prove that v is regular. This extends the results of…
This paper exposes how to obtain a relation that have to be hold for all free--divergence velocity fields that evolve according to Navier--Stokes equations. However, checking the violation of this relation requires a huge computational…
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…
In the given paper, we confront three finite difference approximations to the Navier--Stokes equations for the two-dimensional viscous incomressible fluid flows. Two of these approximations were generated by the computer algebra assisted…
Smooth solutions to the axially symmetric Navier-Stokes equations obey the following maximum principle:$\|ru_\theta(r,z,t)\|_{L^\infty}\leq\|ru_\theta(r,z,0)\|_{L^\infty}.$ We first prove the global regularity of solutions if…
Here we prove the existence of global in time regular solutions to the two-dimensional compressible Navier-Stokes equations supplemented with arbitrary large initial velocity $v\_0$ and almost constantdensity $\varrho\_0$, for large volume…
In this paper, we study the dynamic stability of the 3D axisymmetric Navier-Stokes Equations with swirl. To this purpose, we propose a new one-dimensional (1D) model which approximates the Navier-Stokes equations along the symmetry axis. An…
This paper introduces a novel class of initial data for which the three-dimensional incompressible Navier--Stokes equations yield unique global-in-time solutions. Building on a logarithmically improved regularity criterion, we impose a…
In this paper, we investigate the vanishing viscosity limit problem for the 3-dimensional (3D) incompressible Navier-Stokes equations in a general bounded smooth domain of $R^3$ with the generalized Navier-slip boundary conditions…
We are concerned with existence of regular solutions for non-Newtonian fluids in dimension three. For a certain type of non-Newtonian fluids we prove local existence of unique regular solutions, provided that the initial data are…
We obtain a pointwise, a priori bound for the vorticity of axis symmetric solutions to the 3 dimensional Navier-Stokes equations. The bound is in the form of a reciprocal of a power of the distance to the axis of symmetry. This seems to be…
Systems of hydrodynamic type equations derived from the Navier-Stokes equations and the boundary layer equations are considered. A transformation of the Crocco type reducing the equation order for the longitudinal velocity component is…
In this paper, we consider the inhomogeneous Dirichlet boundary value problem for the stationary Navier--Stokes equations in $n$-dimensional half spaces $\mathbb{R}^n_+= \{ x=(x',x_n)\ ;\ x' \in \mathbb{R}^{n-1}, x_n > 0 \}$ with $n \geq 3$…
Considering the three-dimensional incompressible Navier-Stokes equations on the whole space, we address the question: is it possible to infer global regularity of a mild solution from a single approximate solution? Assuming a relatively…
In this paper, we establish the well-posedness results of the three dimensional stationary Navier--Stokes equations (SNS) in some critical hybrid type Besov spaces with respect to the scaling invariant structure of (SNS). Although such…