相关论文: Local regularity criteria in terms of one velocity…

We are concerned with local regularity of the solutions for the Stokes and Navier-Stokes equations near boundary. Firstly, we construct a bounded solution but its normal derivatives are singular in any $L^p$ with $1<p$ locally near…

In this paper, we establish $\varepsilon$-regularity criteria at one scale for suitable weak solutions to the five dimensional stationary incompressible Navier-Stokes equations in both the unit ball $B_1$ and the unit half ball $B_1^+$,…

We study Liouville-type results for the stationary Navier--Stokes equations in $\mathbb{R}^3$. We prove that any $\dot{H}^1(\mathbb{R}^3)$ solution is trivial under an integrability condition imposed only on the radial component of the…

Two regularity criteria are established to highlight which Littlewood-Paley frequencies play an essential role in possible singularity formation in a Leray-Hopf weak solution to the Navier-Stokes equations in three spatial dimensions. One…

We give new a priori assumptions on weak solutions of the Navier-Stokes equation so as to be able to conclude that they are smooth. The regularity criteria are given in terms of mixed radial-angular weighted Lebesgue space norms.

In this paper, we investigate some priori estimates to provide the critical regularity criteria for incompressible Navier-Stokes equations on $\mathbb{R}^3$ and super critical surface quasi-geostrophic equations on $\mathbb{R}^2$.…

This article is devoted to a regularity criteria for solutions of the Navier-Stokes equations in terms of regularity along the stream lines. More precisely, we prove that a suitable weak solution for the Navier-Stokes equations is regular…

We consider the Navier-Stokes equations in $\mathbb{R}^3$ subject to the initial condition with initial velocity field in $L^{2}_{\rm loc} (\mathbb{R}^3)$ such that $\limsup_{R \to +\infty } R^{-1} \|u_{0} \|_{ L^{2}(B(R))} < +\infty$. Our…

In this paper, we study the regularity problem of the 3D incompressible Navier\~nStokes equations. We prove that the strong solution exists globally for new regularity criteria. For negligible forces, we give an improvement of the known…

In this article, we establish several almost critical regularity conditions such that the weak solutions of the 3D Navier-Stokes equations become regular, based on one component of the solutions, say $u_3$ and $\partial_3u_3$.

We find a global a priori estimate for solutions to the Navier-Stokes equations with periodic boundary conditions guaranteeing in view of the Serrin type condition the existence of global regular solutions. We derive the following estimate…

We consider the axisymmetric Navier-Stokes equations in a finite cylinder $\Omega\subset\R^3$. We assume that $v_r$, $v_\varphi$, $\omega_\varphi$ vanish on the lateral part of boundary $\partial\Omega$ of the cylinder, and that $v_z$,…

In this paper, we are concerned with the partial regularity of the suitable weak solutions to the fractional MHD equations in $\mathbb{R}^{n}$ for $n=2,\,3$. In comparison with the work of the 3D fractional Navier-Stokes equations obtained…

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…

This paper is concerned with geometric regularity criteria for the Navier-Stokes equations in $\mathbb{R}^3_{+}\times (0,T)$ with no-slip boundary condition, with the assumption that the solution satisfies the `ODE blow-up rate' Type I…

In this article we present a Lady{\v{z}}enskaja-Prodi-Serrin Criteria for regularity of solutions for the Navier-Stokes equation in three dimensions which incorporates weak $L^p$ norms in the space variables and log improvement in the time…

We show that any weak solution to the full Navier-Stokes-Fourier system emanating from the data belonging to the Sobolev space W^{3,2} remains regular as long as the velocity gradient is bounded. The proof is based on the weak-strong…

A three-dimensional chemotaxis-Navier-Stokes system is considered. It is known that for all suitably regular initial data, a corresponding initial-boundary value problem admits at least one global weak solution which can be obtained as the…

The aim of the note is to proof a regularity result for weak solutions to the Navier-Stokes equations that are locally in $L_\infty(L^{3,\infty})$. It reads that, in a sense, the number of singular points at each time is at most finite. Our…

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…