Related papers: On the Euler+Prandtl expansion for the Navier-Stok…
For steady two-dimensional flows with a single eddy (i.e. nested closed streamlines), Prandtl (1905) and Batchelor (1956) proposed that in the limit of vanishing viscosity the vorticity is constant in an inner region separated from the…
We consider the incompressible Navier-Stokes and Euler equations in a bounded domain with non-characteristic boundary condition, and study the energy dissipation near the outflow boundary in the zero-viscosity limit. We show that in a…
We use the general exact solution of the Cauchy problem for the compressible Euler vortex equation in unbounded space which was obtained earlier (S.G.Chefranov, Sov. Phys. Dokl., 36, 286, 1991). This solution loses its smoothness in finite…
In [1], T. Clopeau, A. Mikeli\'c, and R. Robert studied the inviscid limit of the 2D incompressible Navier-Stokes equations in a bounded domain subject to Navier friction-type boundary conditions. They proved that the inviscid limit…
Consider the steady solution to the incompressible Euler equation $\bar u=Ae_1$ in the periodic tunnel $\Omega=\mathbb T^{d-1}\times(0,1)$ in dimension $d=2,3$. Consider now the family of solutions $u^\nu$ to the associated Navier-Stokes…
Different authors had received a lot of results regarding the Euler and Navier-Stokes equations. Existence and smoothness of solution for the Navier-Stokes equations in two dimensions have been known for a long time. Leray showed that the…
We prove the existence of a unique local strong solution to the stochastic compressible Euler system with nonlinear multiplicative noise. This solution exists up to a positive stopping time and is strong in both the PDE and probabilistic…
In this paper, we establish the unique existence and some decay properties of a global solution of a free boundary problem of the incompressible Navier-Stokes equations in $L_p$ in time and $L_q$ in space framework in a uniformly…
In this paper we introduce (I,J) similar method for incompressible two and three dimensional Euler equations and Navier-Stokes equations, obtain a series of explicit (I,J) similar solutions to the incompressible two dimensional Euler…
We investigate the existence and the zero viscosity limit of steady compressible shear flow with Navier-slip boundary condition in the absence of any external force in a two-dimension domain $\Omega=(0,L)\times(0,2)$. More precisely, under…
We consider variational principles related to V. I. Arnold's stability criteria for steady-state solutions of the two-dimensional incompressible Euler equation. Our goal is to investigate under which conditions the quadratic forms defined…
We investigate the hydrostatic approximation of a hyperbolic version of Navier-Stokes equations, which is obtained by using Cattaneo type law instead of Fourier law, evolving in a thin strip $\R\times (0,\varepsilon)$. The formal limit of…
We derive the 1D isentropic Euler and Navier-Stokes equations describing the motion of a gas through a nozzle of variable cross section as the asymptotic limit of the 3D isentropic Navier-Stokes system in a cylinder, the diameter of which…
In this article, we study the solutions of the damped Navier--Stokes equation with Navier boundary condition in a bounded domain $\Omega$ in $\mathbb{R}^3$ with smooth boundary. The existence of the solutions is global with the damped term…
This is the first of a series of papers devoted to the initial value problem for the Euler system of compressible fluids and augmented versions containing higher-order terms. We encompass solutions that have finite total energy and enjoy a…
For periodic initial data with the density allowing vacuum, we establish the global existence and exponential decay of weak, strong and classical solutions to the two-dimensional(2D) compressible Navier-Stokes equations when the bulk…
The objective of this work is to present the existence result for the evolu- tionary compressible Navier-Stokes equations via time discretization. We consider the two-dimensional case with slip boundary conditions. First, the existence of…
The first two sections of this work review the framework of [6] for approximate solutions of the incompressible Euler or Navier-Stokes (NS) equations on a torus T^d, in a Sobolev setting. This approach starts from an approximate solution…
In this paper, we investigate the vanishing viscosity limit for the 3D nonhomogeneous incompressible Navier-Stokes equations with a slip boundary condition. We establish the local well-posedness of the strong solutions for initial boundary…
The Voight regularization of the Navier--Stokes system is studied in a bounded domain and on the torus. In the 3D case we obtain new explicit bounds for the attractor dimension improving the previously known results. In the 2D case we show…