相关论文: Navier-Stokes' equations for radial and tangential…

We examine the Navier-Stokes equations with homogeneous slip boundary conditions coupled with the heat equation with homogeneous Neumann conditions in a bounded domain in $R^3$. The considered domain is a cylinder with $x_3$-axis. The aim…

Consider the three-dimensional Navier--Stokes flow past a moving rigid body $\mathscr{O} \subset \mathbb{R}^3$ with prescribed translational and angular velocities, where $\mathscr{O}$ stands for a bounded Lipschitz domain. We prove that…

The instant Lagranian coordinator system is used to describe the fluid material motion. By this way, the instant deformation gradient (expressed by spatial velocity gradient) concept is established. Based on this geometrical understanding,…

The incompressible Navier-Stokes equations and static Euler equations are considered. We find that there exist infinite non-trivial regular solutions of incompressible static Euler equations with given boundary conditions. Moreover there…

This paper provides primarily an analytical ad hoc -solution for 3-dimensional, incompressible Navier-Stokes equations with a suitable external force field. The solution turns out to be smooth and integrable on the whole space. There is…

We develop a new formalism for the study of turbulence using the scale relativity framework (applied in $v$-space according to de Montera's proposal). We first review some of the various ingredients which are at the heart of the scale…

A new fourth order compact formulation for the steady 2-D incompressible Navier-Stokes equations is presented. The formulation is in the same form of the Navier-Stokes equations such that any numerical method that solve the Navier-Stokes…

The proposal for a new formulation of the Navier-Stokes equations is based on a Helmholtz-Hodge decomposition where all the terms corresponding to the physical phenomena are written as the sum of a divergence-free term and another curl-free…

We study the 2D Navier-Stokes equations within the framework of a constraint that ensures energy conservation throughout the solution. By employing the Galerkin approximation method, we demonstrate the existence and uniqueness of a global…

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…

We show that non-uniqueness of the Leray-Hopf solutions of the Navier--Stokes equation on the hyperbolic plane observed in arXiv:1006.2819 is a consequence of the Hodge decomposition. We show that this phenomenon does not occur on the…

Large weak solutions to Navier--Stokes--Maxwell systems are not known to exist in their corresponding energy space in full generality. Here, we mainly focus on the three-dimensional setting of a classical incompressible…

We develop a mesh-based semi-Lagrangian discretization of the time-dependent incompressible Navier-Stokes equations with free boundary conditions recast as a non-linear transport problem for a momentum 1-form. A linearly implicit fully…

A fundamental problem in analysis is to decide whether a smooth solution exists for the Navier-Stokes equations in three dimensions. In this paper we shall study this problem. The Navier-Stokes equations are given by:…

We study the weak boundary layer phenomenon of the Navier-Stokes equations in a 3D bounded domain with viscosity, $\epsilon > 0$, under generalized Navier friction boundary conditions, in which we allow the friction coefficient to be a (1,…

The dynamics defined by the Navier-Stokes equations under the Marangoni boundary conditions in a two dimensional domain is considered. This model of fluid dynamics involve fundamental physical effects: convection, diffusion and capillary…

In the present work, we investigate a numerical one-dimensional solver to the Navier-Stokes equation that retains all terms, including both pressure and dissipation. Solutions to simple examples that illustrate the actions of the nonlinear…

We study stochastic Navier-Stokes equations in two dimensions with respect to periodic boundary conditions. The equations are perturbed by a nonlinear multiplicative stochastic forcing with linear growth (in the velocity) driven by a…

In this paper, we study the inviscid limit of the free surface incompressible Navier-Stokes equations with or without surface tension. By delicate estimates, we prove the weak boundary layer of the velocity of the free surface Navier-Stokes…

Motivated by the classification of solutions of harmonic functions, we investigate Liouville type theorems for the fractional Navier-Stokes equations in $\mathbb{R}^3$ under some conditions on the boundedness of fractional derivatives. We…