Related papers: The regularity criterion for 3D Navier-Stokes Equa…
In the paper, a new {\it slightly supercritical} condition, providing {\it local} regularity of axially symmetric solutions to the non-stationary 3D Navier-Stokes equations, is discussed. It generalises almost all known results in the local…
In this paper we prove the logarithmically improved Serrin's criteria to the three-dimensional incompressible Navier-Stokes equations.
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 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 consider a family of 3D models for the axi-symmetric incompressible Navier-Stokes equations. The models are derived by changing the strength of the convection terms in the axisymmetric Navier-Stokes equations written using a set of…
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 give a new concise proof of a certain one-scale epsilon regularity criterion using weak-strong uniqueness for solutions of the Navier-Stokes equations with non-zero boundary conditions. It is inspired by an analogous approach for the…
In this paper, we study the three-dimensional axisymmetric Navier-Stokes system with nonzero swirl. By establishing a new key inequality for the pair $(\frac{\omega^{r}}{r},\frac{\omega^{\theta}}{r})$, we get several Prodi-Serrin type…
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…
In this paper, we consider the conditional regularity of weak solution to the 3D Navier--Stokes equations. More precisely, we prove that if one directional derivative of velocity, say $\partial_3 u,$ satisfies $\partial_3 u \in…
In this small note we strengthen the classic result about the regularity time t* of arbitrary Leray solutions to the (incompressible) Navier-Stokes equations in Rn (n = 3, 4), which have the form: t* <= K_{3} nu^{-5} || u(.,0) ||_{L2}^{4}…
Considering the three-dimensional incompressible Navier-Stokes equations on the whole space, we address the question: is it possible to infer global regularity of a mild solution from a single approximate solution? Assuming a relatively…
This is an expository paper on the theory of local regularity for weak solutions to the non-stationary 3D Navier-Stokes equations near the boundary of a domain.
We study the Navier-Stokes equations with an extra eddy viscosity term in the whole space in three dimensions. We introduce a suitable regularized system for which we prove the existence of a regular solution defined for all time. We prove…
In this paper we consider the three-dimensional Navier-Stokes equations in an infinite channel. We provide a sufficient condition, in terms of $\partial_z p$, where $p$ is the pressure, for the global existence of the strong solutions to…
The Navier--Stokes system is considered in a compact Riemannian manifold. Gevrey class regularity is proven under Lions boundary conditions: in 2D for the Rectangle, Cylinder, and Hemisphere, and in 3D for the Rectangle. The cases of the 2D…
In this paper, we give a brief survey of recent results on axially symmetric Navier-Stokes equations (ASNS) in the following categories: regularity criterion, Liouville property for ancient solutions, decay and vanishing of stationary…
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 $\mathbb{R}^2$.…
We show that if v is an axially symmetric suitable weak solution to the Navier Stokes equations (in the sense of L. Caffarelli, R. Kohn & L. Nirenberg) such that the radial component of v has a higher regularity (i.e. satisfies weighted…
In this paper we propose new method for proving of global solutions for 3D Navier-Stokes equations. This complies an application to the Clay Institute Millennium Prize Navier Stokes Problem. The proposed method can be applied for…