Related papers: The Steady Boltzmann and Navier-Stokes Equations

This paper is concerned with the evolution of the periodic boundary value problem and the mixed boundary value problem for a compressible mixture of binary fluids modeled by the Navier-Stokes-Cahn-Hilliard system in one dimensional space.…

This work deals with the non-cutoff Boltzmann equation for all type of potentials, in both the torus $\mathbf{T}^3$ and in the whole space $\mathbf{R}^3$, under the incompressible Navier-Stokes scaling. We first establish the well-posedness…

This work is devoted to study the global behavior of viscous flows contained in a symmetric domain with complete slip boundary. In such scenario the boundary no longer provides friction and therefore the perturbation of angular velocity…

A thermal convection flow in the three-dimensional unbounded fluid domain exterior to a sphere is considered. The viscosity force is determined by a fractional power of the Stokes operator. A purely conductive steady state arises due to the…

The Navier-Stokes motions in a box with periodic boundary conditions are considered. First the existence of global regular two-dimensional solutions is proved. The solutions are such that continuous with respect to time norms are controlled…

We study the boundary value problem for the stationary Navier--Stokes system in two dimensional exterior domain. We prove that any solution of this problem with finite Dirichlet integral is uniformly bounded. Also we prove the existence…

We consider a flow of non-Newtonian incompressible heat conducting fluids with dissipative heating. Such system can be obtained by scaling the classical Navier--Stokes--Fourier problem. As one possible singular limit may be obtained the…

In this paper, we examine the averaging effect of a highly oscillating external force on the solutions of the Navier-Stokes equations. We show that, as long as the force time-average decays over time, if the frequency and amplitude of the…

In this paper we study the vanishing viscosity limit for the inhomogeneous incompressible Navier-Stokes equations on bounded domains with no-slip boundary condition in two or three space dimensions. We show that, under suitable assumptions…

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 this paper, we consider the 1D Navier-Stokes equations for viscous compressible and heat conducting fluids (i.e., the full Navier-Stokes equations). We get a unique global classical solution to the equations with large initial data and…

In this work, we investigate the small-time global exact controllability of the Navier-Stokes equation, both towards the null equilibrium state and towards weak trajectories. We consider a viscous incompressible fluid evolving within a…

The Navier-Stokes equations in the primitive formulation for incompressible flow describe the evolution of velocity and pressure, without recourse to vorticity. We show that, beyond the finite Leray-Hopf regularity interval, every…

The paper examines the issue of existence of solutions to the steady Navier-Stokes equations in an exterior domain in $\mathbb{R}^2$. The system is studied with nonhomogeneous slip boundary conditions. The main results proves the existence…

We propose a kinetic framework for single-component non-ideal isothermal flows. Starting from a kinetic model for a non-ideal fluid, we show that under conventional scaling the Navier-Stokes equations with a non-ideal equation of state are…

The predictive accuracy of the Navier-Stokes equations is known to degrade at the limits of the continuum assumption, thereby necessitating expensive and often highly approximate solutions to the Boltzmann equation. While tractable in one…

This paper concerns an initial boundary value problem of compressible Navier-Stokes-Poisson equations with the non-flat doping profile in a 3-D exterior domain.The global existence of strong solutions near a steady state for compressible…

We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally speaking, the proof is based on the new weighted…

This paper is concerned with the study of the nonlinear stability of the contact discontinuity of the Navier-Stokes-Poisson system with free boundary in the case where the electron background density satisfies an analogue of the Boltzmann…

We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…