相关论文: Three regularization models of the Navier-Stokes e…

This study aims to identify the properties, advantages, and drawbacks of some common (and some less common) sub-grid scale (SGS) models for large eddy simulation of low Mach compressible flows using high order spectral elements. The models…

This paper concerns the existence of global weak solutions \`a la Leray for compressible Navier-Stokes equations with a pressure law that depends on the density and on time and space variables $t$ and $x$. The assumptions on the pressure…

We consider a modification of the three-dimensional Navier--Stokes equations and other hydrodynamical evolution equations with space-periodic initial conditions in which the usual Laplacian of the dissipation operator is replaced by an…

If $u$ is a Leray-Hopf solution to the Navier-Stokes equations with the initial data in $ L^2(\mathbb{R}^3)$, then $u$ is regular.

We study the three-dimensional incompressible Navier-Stokes system on $\mathbb{R}^3$ with an additional dissipative nonlocal term \[ \partial_t u + (u\cdot\nabla)u + \nabla p = \nu \Delta u + Lu, \qquad {\rm div}\, u = 0, \] where $L$ is a…

In 1987, Michael Wiegner in his seminal paper [17] provided an important result regarding the energy decay of Leray solutions $\boldsymbol u(\cdot,t)$ to the incompressible Navier-Stokes in $\mathbb{R}^{n}$: if the associated Stokes flows…

It is well-known that the Rayleigh--Taylor (abbr. RT) instability can be completely inhibited by the quantum effect stabilization in proper circumstances leading to a cutoff wavelength in the \emph{linear} motion equations. Motivated by the…

The asymptotic behavior of solutions of the three-dimensional Navier-Stokes equations is considered on bounded smooth domains with no-slip boundary conditions or on periodic domains. Asymptotic regularity conditions are presented to ensure…

The Navier-Stokes-Cahn-Hilliard (NSCH) system governs the diffuse-interface dynamics of two incompressible and immiscible fluids. We consider a relaxation approximation of the NSCH system that is composed by a system of first-order…

We prove a local-in-time regularity criterion for the 3D Navier-Stokes equations. In particular, it follows from the criterion that the Hausdorff dimension of possible singular times of Leray-Hopf weak solutions $u\in L^r_t…

In the present study, the efficiency of preconditioners for solving linear systems associated with the discretized variable-density incompressible Navier-Stokes equations with semiimplicit second-order accuracy in time and spectral accuracy…

The first goal of this paper is to study the large time behavior of solutions to the Cauchy problem for the 3-dimensional incompressible Navier-Stokes system. The Marcinkiewicz space $L^{3,\infty}$ is used to prove some asymptotic stability…

This paper presents a Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) method for solving the two-equation Reynolds-Averaged Navier-Stokes (RANS) model. The turbulent wall-bounded flow with or without mild flow separation, a…

The compressible Navier-Stokes-Allen-Cahn system models the motion of a mixture of two macroscopically immiscible viscous compressible fluids. In this paper, we are concerned with the large time behavior of solutions to the Cauchy problem…

We propose a microlocal-Riemannian framework for the three-dimensional incompressible Navier-Stokes equations on a smooth oriented Riemannian manifold (M,g). The dynamics is lifted to the unit cosphere bundle S*M via a normal-coordinate…

A well-known diffuse interface model consists of the Navier-Stokes equations nonlinearly coupled with a convective Cahn-Hilliard type equation. This system describes the evolution of an incompressible isothermal mixture of binary-fluids and…

For wavenumbers k such that k * alpha > 1, corresponding to spatial scales smaller than alpha, there are three candidate power laws for the energy spectrum of the Navier-Stokes-alpha model, corresponding to three possible dynamical eddy…

A modified version of the three dimensional Navier-Stokes equations is considered with periodic boundary conditions. A bounded constant delay is introduced into the convective term, that produces a regularizing effect on the solution. In…

The aim of this paper is to describe the long time behavior of solutions of linearized Navier Stokes equations near a concave shear layer profile in the long waves regime, namely for small horizontal Fourier variable $\alpha$, when the…

In this paper, existence of generalized solutions to a thermodynamically consistent Navier--Stokes--Cahn--Hilliard model introduced in [18] is proven in any space dimension. The generalized solvability concepts are measure-valued and…