相关论文: Remarks on a quasi-linear model of the Navier-Stok…
We review the properties of the nonlinearly dispersive Navier-Stokes-alpha (NS-alpha) model of incompressible fluid turbulence -- also called the viscous Camassa-Holm equations and the LANS equations in the literature. We first re-derive…
Self-similar Euler singularities may be useful for understanding some aspects of Navier-Stokes turbulence. Here, a causal explanation for intermittency is given, based on the control of the sudden growth of the gradients by the Euler…
Turbulence governed by the Navier-Stokes equations shows a tendency to evolve towards a state in which the nonlinearity is diminished. In fully developed turbulence this tendency can be measured by comparing the variance of the nonlinear…
Coherent structures/motions in turbulence inherently give rise to intermittent signals with sharp peaks, heavy-skirt, and skewed distributions of velocity increments, highlighting the non-Gaussian nature of turbulence. That suggests that…
Following the Gallavotti's conjecture, Stationary states of Navier-Stokes fluids are proposed to be described equivalently by alternative equations besides the NS equation itself. We propose a model system symmetric under time-reversal…
We show that the problem of non conservation of energy found in the spontaneous localization model developed by Ghirardi, Rimini and Weber is very similar to the inconsistency between the stochastic models for turbulence and the…
A system of partial differential equations for a diffusion interface model is considered for the stationary motion of two macroscopically immiscible, viscous Newtonian fluids in a three-dimensional bounded domain. The governing equations…
We consider the motion of an incompressible viscous fluid on a compact Riemannian manifold $\sM$ with boundary. The motion on $\sM$ is modeled by the incompressible Navier-Stokes equations, and the fluid is subject to pure or partial slip…
The Navier-Stokes equations are paradigmatic equations describing hydrodynamics of an interacting system with microscopic interactions encoded in transport coefficients. In this work we show how the Navier-Stokes equations arise from the…
We analyze the forced incompressible stationary Navier-Stokes flow in $\mathbb{R}^n_+$, $n>2$. Existence of a unique solution satisfying a global integrabilty property measured in a scale of tent spaces is established for small data in…
Recent studies suggest that unstable, non-chaotic solutions of the Navier-Stokes equation may provide deep insights into fluid turbulence. In this article, we present a combined experimental and numerical study exploring the dynamical role…
The concept of continuous topological evolution, based upon Cartan's methods of exterior differential systems, is used to develop a topological theory of non-equilibrium thermodynamics, within which there exist processes that exhibit…
We investigate in the present paper the Navier-Stokes equations on quantum Euclidean spaces $\mathbb{R}^d_{\theta}$ with $\theta$ being a $d\times d$ antisymmetric matrix, which is a standard example of non-compact noncommutative manifolds.…
In this paper, we investigate the instability of the trivial steady states to the incompressible viscous fluid with Navier-slip boundary conditions. For the linear instability, the existence of infinitely many normal mode solutions to the…
Mechanical effects that span multiple physical scales -- such as the influence of vanishing molecular viscosity on large-scale flow structures under specific conditions -- play a critical role in real fluid systems. The spin angular…
The interaction between a viscous fluid and an elastic solid is modeled by a system of parabolic and hyperbolic equations, coupled to one another along the moving material interface through the continuity of the velocity and traction…
This is an expository paper on the theory of local regularity for weak solutions to the non-stationary 3D Navier-Stokes equations near the boundary of a domain.
A phenomenological turbulence model in which the energy spectrum obeys a nonlinear diffusion equation is presented. This equation respects the scaling properties of the original Navier-Stokes equations and it has the Kolmogorov -5/3 cascade…
Exponential stabilizability of the incompressible Navier-Stokes equations under dynamic slip boundary conditions toward arbitrary time-dependent trajectories is proven. The feedback control law is constructed explicitly using oblique…
In order to understand whether, and to what extent, spectral representation can effectively highlight the nonlinear interaction among different scales, it is necessary to consider the state that precedes the onset of instabilities and…