Related papers: Navier-Stokes equations in the half space with non…
We examine the conditional regularity of the solutions of Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axially symmetric. We show that if positive part of the radial component of…
This paper is dedicated to the construction of global weak solutions to the quantum Navier-Stokes equation, for any initial value with bounded energy and entropy. The construction is uniform with respect to the Planck constant. This allows…
Non-linear entropy stability and a summation-by-parts framework are used to derive entropy stable wall boundary conditions for the three-dimensional compressible Navier--Stokes equations. A semi-discrete entropy estimate for the entire…
We consider the Euler system of gas dynamics endowed with the incomplete equation of state relating the internal energy to the mass density and the pressure. We show that any sufficiently smooth solution can be recovered as a vanishing…
We prove the existence of relative finite-energy vanishing viscosity solutions of the one-dimensional, isentropic Euler equations under the assumption of an asymptotically isothermal pressure law, that is, $p(\rho)/\rho = O(1)$ in the limit…
We construct global weak solutions of the Euler equations in an infinite cylinder $\Pi=\{x\in \mathbb{R}^{3}\ |\ x_h=(x_1,x_2),\ r=|x_h|<1\}$ for axisymmetric initial data without swirl when initial vorticity…
We consider the initial-value problem in the $d$-dimensional Euclidean space $\mathbb{R}^d$ $(d \ge 3)$ for the compressible Navier-Stokes-Korteweg equations under the zero sound speed case (namely, $P'(\rho_*)=0$, where $P=P(\rho)$ stands…
We develop the concept of an infinite-energy statistical solution to the Navier-Stokes and Euler equations in the whole plane. We use a velocity formulation with enough generality to encompass initial velocities having bounded vorticity,…
In this paper, we will prove a new result that guarantees the global existence of solutions to the Navier--Stokes equation in three dimensions when the initial data is sufficiently close to being two dimensional. This result interpolates…
In this work, we establish a class of globally defined, large solutions to the free boundary problem of compressible Navier-Stokes equations with constant shear viscosity and vanishing bulk viscosity. We establish such solutions with…
For the initial boundary value problem of compressible barotropic Navier-Stokes equations in one-dimensional bounded domains with general density-dependent viscosity and large external force, we prove that there exists a unique global…
The two-phase free boundary value problem for the isothermal Navier-Stokes system is studied for general bounded geometries in absence of phase transitions, external forces and boundary contacts. It is shown that the problem is well-posed…
In this article we consider viscous flow in the exterior of an obstacle satisfying the standard no-slip boundary condition at the surface of the obstacle. We seek conditions under which solutions of the Navier-Stokes system in the exterior…
Assume no-slip boundary conditions for the velocity field and either insulated or Dirichlet boundary conditions for the temperature field in a steady compressible fluid. In the inviscid limit $\v \rightarrow 0$, we develop a mathematical…
In this paper, we investigate the existence of a unique global smooth solution to the three-dimensional incompressible Navier-Stokes equations and provide a concise proof. We establish a new global well-posedness result that allows the…
H.-O. Bae and H.J. Choe, in a 1997 paper, established a regularity criteria for the incompressible Navier-Stokes equations in the whole space $\R^3$ based on two velocity components. Recently, one of the present authors extended this result…
In this paper, we study the initial value problem of the Navier-Stokes equations in the half-space. Let a solenoidal initial velocity be given in the function space $ \dot{B}_{pq,0}^{\alpha-\frac{2}{2}}({\mathbb R}^n_+)$ for $\alpha +1 =…
In this paper, we generalize the main results of [1] and [31] to Lorentz spaces, using a simple procedure. The main results are the following. Let $n\geq 3$ and let $u$ be a Leray-Hopf solution to the $n$-dimensional Navier-Stokes equations…
We propose and analyse an augmented mixed finite element method for the Navier--Stokes equations written in terms of velocity, vorticity, and pressure with non-constant viscosity and no-slip boundary conditions. The weak formulation…
Recently, A. Vasseur and C. Yu have proved the existence of global entropy-weak solutions to the compressible Navier-Stokes equations with viscosities $\nu(\varrho)=\mu\varrho$ and $\lambda(\varrho)=0$ and a pressure law under the form…