相关论文: Pressure Regularity Criterion for the Three-dimens…

In this paper, we investigate the incompressible steady Navier-Stokes system with no-slip boundary condition in a two-dimensional channel. Given any flux, the existence of solutions is proved as long as the width of cross-section of the…

The nonhomogeneous Navier-Stokes equations are considered in a cylindrical domain in ${\mathbb R}^3$, parallel to the $x_3$-axis with large inflow and outflow on the top and the bottom. Moreover, on the lateral part of the cylinder the slip…

Consider an axis-symmetric suitable weak solution of 3D incompressible Navier-Stokes equation with nontrivial swirl. If the solution satisfies a slightly supercritical assumption, we will prove that v is regular. This extends the results of…

We first show the equivalence of two classes of generalized suitable weak solutions to the 3D incompressible Navier-Stokes equations allowing distributional pressure, the class of dissipative weak solutions and local suitable weak…

We consider the Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under Navier's slip boundary conditions. When the thickness of the thin domain is sufficiently small, we establish the global…

We construct solutions to the randomly-forced Navier--Stokes--Poisson system in periodic three-dimensional domains or in the whole three-dimensional Euclidean space. These solutions are weak in the sense of PDEs and also weak in the sense…

We identify a sufficient condition under which solutions to the 3D forced Navier--Stokes equations satisfy an $L^p$-in-time version of the Kolmogorov 4/5 law for the behavior of the averaged third order longitudinal structure function along…

We consider the three-dimensional steady Navier-Stokes system in the exterior of an infinite cylinder under the action of an external force. We construct solutions in the class of vertically uniform flows which vanish at horizontal…

In this paper, we are concerned with the global existence and stability of a 3-D perturbed viscous circulatory flow around an infinite long cylinder. This flow is described by 3-D compressible Navier-Stokes equations. By introducing some…

The incompressible Navier-Stokes equations are considered. We find that there exist infinite non-trivial solutions of static Euler equations. Moreover there exist random solutions of static Euler equations. Provided Reynolds number is large…

We present some new regularity criteria for ``suitable weak solutions'' of the Navier-Stokes equations near the boundary in dimension three. We prove that suitable weak solutions are H\"older continuous up to the boundary provided that the…

In this paper, we consider the three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity in presence of vacuum over bounded domains. Global-in-time unique strong solution is proved to exist when $\|\nabla…

The Navier-Stokes equations in a finite cylinder are written in terms of poloidal and toroidal potentials in order to impose incompressibility. Regularity of the solutions is ensured in several ways: First, the potentials are represented…

We prove, with a more geometric approach, that the solutions to the Navier-Stokes equations are regular up to a set of Hausdorff dimension 1. The main tool for the proof is a new compactness lemma and the monotonicity property of harmonic…

We prove the existence of the weak solutions to the compressible Navier--Stokes system with barotropic pressure $p(\varrho)=\varrho^\gamma$ for $\gamma\geq 9/5$ in three space dimension. The novelty of the paper is the approximation scheme…

This paper is devoted to presenting new interior regularity criteria in terms of one velocity component for weak solutions to the Navier-Stokes equations in three dimensions. It is shown that the velocity is regular near a point $z$ if its…

This paper concerns the barotropic compressible Navier-Stokes equations in a two-dimensional half-space subject to Navier-slip boundary conditions with vacuum or non-vacuum far-field density. The global existence and large-time behavior of…

Smooth solutions to the axially symmetric Navier-Stokes equations obey the following maximum principle:$\|ru_\theta(r,z,t)\|_{L^\infty}\leq\|ru_\theta(r,z,0)\|_{L^\infty}.$ We first prove the global regularity of solutions if…

We show that any smooth stationary solution of the 3D incompressible Navier-Stokes equations in the whole space, the half space, or a periodic slab must vanish under the condition that for some $0 \le \delta \le 1<L$ and…

We show that in bounded domains with no-slip boundary conditions, the Navier-Stokes pressure can be determined in a such way that it is strictly dominated by viscosity. As a consequence, in a general domain we can treat the Navier-Stokes…