相关论文: Microscopic statistical description of incompressi…
An aspect of fluid dynamics lies in the search of possible statistical models for Navier-Stokes (NS) fluids described by classical solutions of the incompressible Navier-Stokes equations (INSE). This refers in particular to statistical…
A remarkable feature of fluid dynamics is its relationship with classical dynamics and statistical mechanics. This has motivated in the past mathematical investigations concerning, in a special way, the "derivation" based on kinetic theory,…
Fundamental aspects of fluid dynamics are related to construction of statistical models for incompressible Navier-Stokes fluids. The latter can be considered either \textit{deterministic} or \textit{stochastic,} respectively for…
We study the Navier-Stokes equations governing the motion of isentropic compressible fluid in three dimensions driven by a multiplicative stochastic forcing. In particular, we consider a stochastic perturbation of the system as a function…
In the continuum flow regime, the Navier-Stokes equations are usually used for the description of gas dynamics. On the other hand, the Boltzmann equation is applied for the rarefied gas dynamics. Both equations are constructed from modeling…
The relation between Latttice Boltzmann Method, which has recently become popular, and the Kinetic Schemes, which are routinely used in Computational Fluid Dynamics, is explored. A new discrete velocity model for the numerical solution of…
In the theory of the Navier-Stokes equations, the viscous fluid in incompressible flow is modelled as a homogeneous and dense assemblage of constituent "fluid particles" with viscous stress proportional to rate of strain. The crucial…
We consider the hydrodynamic limits of the quantum Boltzmann equation with Fermi-Dirac statistics for hard sphere and hard potentials in the whole space. By analyzing the spectrum of the linearized collision operator combined with the…
The incompressible Navier-Stokes equations coupled to the Maxwell-Stefan relations for the molar fluxes are analyzed in bounded domains with no-flux boundary conditions. The system models the dynamics of a multicomponent gaseous mixture…
In this paper the problem of strong solvability of the incompressible Navier-Stokes equations (INSE) is revisited, with the goal of determining the minimal assumptions for the validity of a local existence and uniqueness theorem for the…
We establish the incompressible Navier--Stokes limit for the discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighborhood of the global Maxwellian.…
The article provides an analytical solution of the Navier-Stokes equations for the case of the steady flow of an incompressible fluid between two uniformly co-rotating disks. The solution is derived from the asymptotical evolution of…
An open problem arising in the statistical description of turbulence is related to the \textit{theoretical prediction based on first principles} of the so-called multi-point velocity probability density functions (PDFs) characterizing a…
This paper studies global existence, hydrodynamic limit, and large-time behavior of weak solutions to a kinetic flocking model coupled to the incompressible Navier-Stokes equations. The model describes the motion of particles immersed in a…
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…
Fundamental aspects of inverse kinetic theories for incompressible Navier-Stokes equations concern the possibility of defining uniquely the kinetic equation underlying such models and furthermore, the construction of a kinetic theory…
For the water-air system, the bulk density ratio is as high as about 1000; no model can fully tackle such a high density ratio system. In the Navier-Stokes and Euler equations, the density $\rho$ within the water-air interface is assumed to…
A fundamental aspect of turbulence theory is related to the identification of realizable phase-space statistical descriptions able to reproduce in some suitable sense the stochastic fluid equations of a turbulent fluid. In particular, a…
Granular fluids consist of collections of activated mesoscopic or macroscopic particles (e.g., powders or grains) whose flows often appear similar to those of normal fluids. To explore the qualitative and quantitative description of these…
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…