Related papers: A regularity criterion for the weak solutions to t…

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…

We consider the Navier-Stokes-Fourier system with the inhomogeneous boundary conditions for the velocity and the temperature. We show that solutions emanating from sufficiently regular data remain regular as long as the density $\varrho$,…

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…

In this paper, we study regularity of weak solutions to the incompressible Navier-Stokes equations in $\mathbb{R}^{3}\times (0,T)$. The main goal is to establish the regularity criterion via the gradient of one velocity component in…

The Navier-Stokes-Fourier system describing the motion of a compressible, viscous, and heat conducting fluid is known to possess global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides…

We consider the Navier-Stokes-Fourier system with general inhomogeneous Dirichlet-Neumann boundary conditions. We propose a new approach to the local well-posedness problem based on conditional regularity estimates. By conditional…

We consider the Navier--Stokes--Fourier system in a bounded domain $\Omega \subset R^d$, $d=2,3$, with physically realistic in/out flow boundary conditions. We develop a new concept of weak solutions satisfying a general form of relative…

We show that finite-energy weak solutions to the incompressible Navier--Stokes equations on a three-dimensional bounded smooth domain are regular up to the boundary, provided that the $L^4_tL^4_x$-norm of the solution is smaller than a…

In this paper, we address the partial regularity of suitable weak solutions of the incompressible Navier--Stokes equations. We prove an interior regularity criterion involving only one component of the velocity. Namely, if $(u,p)$ is a…

We study local regularity properties of a weak solution $u$ to the Cauchy problem of the incompressible Navier-Stokes equations. We present a new regularity criterion for the weak solution $u$ satisfying the condition…

Several regularity criterions of Leray-Hopf weak solutions $u$ to the 3D Navier-Stokes equations are obtained. The results show that a weak solution $u$ becomes regular if the gradient of velocity component $\nabla_{h}{u}$ (or $…

We prove a weak stability result for the three-dimensional homogeneous incompressible Navier-Stokes system. More precisely, we investigate the following problem : if a sequence $(u_{0, n})_{n\in \N}$ of initial data, bounded in some scaling…

We prove partial regularity of suitable weak solutions to the Navier--Stokes equations at the boundary in irregular domains. In particular, we provide a criterion which yields continuity of the velocity field in a boundary point and obtain…

We present new interior regularity criteria for suitable weak solutions of the 3-D Navier-Stokes equations: a suitable weak solution is regular near an interior point $z$ if either the scaled $L^{p,q}_{x,t}$-norm of the velocity with…

We are concerned with the problem,originated from Seregin [18,19,20], what are minimal sufficiently conditions for the regularity of suitable weak solutions to the 3d Naiver-Stokes equations. We prove some interior regularity criteria, in…

We establish some interior regularity criterions of suitable weak solutions for the 3-D Navier-Stokes equations, which allow the vertical part of the velocity to be large under the local scaling invariant norm. As an application, we improve…

We formulate a new criterion for regularity of a suitable weak solution v to the Navier-Stokes equations at the space-time point (x_0,t_0). The criterion imposes a Serrin-type integrability condition on v only in a backward neighbourhood of…

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 are concerned with regularity of suitable weak solutions of the 3D Navier-Stokes equations in Lorentz spaces. We obtain $\varepsilon$-regularity criteria in terms of either the velocity, the gradient of the velocity, the…

We consider the incompressible Navier-Stokes equations in a moving domain whose boundary is prescribed by a function $\eta=\eta(t,y)$ (with $y\in\mathbb R^2$) of low regularity. This is motivated by problems from fluid-structure…