相关论文: Navier-Stokes equations and fluid turbulence
We consider the hydrodynamics of relativistic conformal field theories at finite temperature. We show that the limit of slow motions of the ideal hydrodynamics leads to the non-relativistic incompressible Euler equation. For viscous…
We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a general domain in $\R^n$ with compact and smooth boundary, subject to the kinematic and vorticity boundary conditions on the non-flat…
We introduce a modification of the Navier-Stokes equation that has the remarkable property of possessing an infinite number of conserved quantities in the inviscid limit. This new equation is studied numerically and turbulence properties…
Heuristic derivations of the Navier-Stokes equations are unable to reveal the applicability limits of these equations. In this paper we rederive the Navier-Stokes equations from kinetic theory, using a method that affords a step by step…
Efficient simulation of the Navier-Stokes equations for fluid flow is a long standing problem in applied mathematics, for which state-of-the-art methods require large compute resources. In this work, we propose a data-driven approach that…
The question at stake in Lagrangian controllability is whether one can move a patch of fluid particles to a target location by means of remote action in a given time interval. In the last two decades, positive results have been obtained…
Turbulent flows are notoriously difficult to describe and understand based on first principles. One reason is that turbulence contains highly intermittent bursts of vorticity and strain-rate with highly non-Gaussian statistics.…
The Clebsch representation of a velocity field represents an effective tool for the analysis of physical properties of fluid flows. Indeed, a suitable choice of Clebsch potentials can be used to extract structural features that would…
This work is based on a formulation of the incompressible Navier-Stokes equations developed by P. Constantin and G.Iyer, where the velocity field of a viscous incompressible fluid is written as the expected value of a stochastic process. If…
We present an analysis of the Navier-Stokes equations based on a spatial filtering technique to elucidate the multi-scale nature of fully developed turbulence. In particular, the advection of a band-pass-filtered small-scale contribution by…
In this article, we introduce a new mathematical framework that can describe the budget of turbulence kinetic energy and heat transfer in both physical space and scale space of turbulence. We derived two exact transport equations for…
We investigate multidimensional model for incompressible non-Newtonian fluids. Using method of energy estimates we prove the property of finite speed of propagations of the solution support for this problem. We find sharp bounds of the…
A rigorous derivation of the incompressible Euler equations with the no-penetration boundary condition from the Boltzmann equation with the diffuse reflection boundary condition has been a challenging open problem. We settle this open…
In these lecture notes, we provide an introduction to the theory of mixing for incompressible flows from a PDE perspective. We discuss both the Lagrangian (ODE) and Eulerian (PDE, continuity equation) viewpoints, and introduce suitable…
The grand potential for open systems describes thermodynamics of fluid flows at low Mach numbers. A new system of reduced equations for the grand potential and the fluid momentum is derived from the compressible Navier-Stokes equations. The…
Time-dependent free surface problem for the incompressible Navier-Stokes equations which describes the motion of viscous incompressible fluid nearly half-space are considered. We obtain global well-posedness of the problem for a small…
We consider the motion of a compressible, viscous, and heat conducting fluid in the regime of small viscosity and heat conductivity. It is shown that weak solutions of the associated Navier- Stokes-Fourier system converge to a (strong)…
The incompressible Navier-Stokes-Fourier system with viscous heating was first derived from the Boltzmann equation in the form of the diffusive scaling by Bardos-Levermore-Ukai-Yang (2008). The purpose of this paper is to justify such an…
The existence of large-data weak solutions to a steady compressible Navier-Stokes-Fourier system for chemically reacting fluid mixtures is proved. General free energies are considered satisfying some structural assumptions, with a pressure…
The paper develops a finite element method for the Navier-Stokes equations of incompressible viscous fluid in a time-dependent domain. The method builds on a quasi-Lagrangian formulation of the problem. The paper provides stability and…