Related papers: A regularity criterion in weak spaces to Boussines…
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…
It establishes a regularity criterion for non-Newtonian fluids in $\mathbb{R}^3$ in terms of the weighted gradient of the velocity field, based on the Caffarelli--Kohn--Nirenberg inequality.
In this paper we establish a Serrin type regularity criterion on the gradient of pressure in weak spaces for the Leray-Hopf weak solutions of the Navier-Stokes equations in R3.
We study the partial regularity of suitable weak solutions to the three dimensional incompressible Navier--Stokes equations. There have been several attempts to refine the Caffarelli--Kohn--Nirenberg criterion (1982). We present an improved…
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…
We study the regularity of a distributional solution $(u,p)$ of the 3D incompressible evolution Navier-Stokes equations. Let $B_r$ denote concentric balls in $\mathbb{R}^3$ with radius $r$. We will show that if $p\in L^{m} (0,1; L^1(B_2))$,…
In this paper, we show the existence of H\"{o}lder continuous periodic weak solutions of the 3D Boussinesq equation with thermal diffusion, which apprroximate the Onsager's critical spatial regularity and satisfy the prescribed kinetic…
In this paper we consider the regularity problem of the Navier-Stokes equations in $ \R^{3} $. We show that the Serrin-type condition imposed on one component of the velocity $ u_3\in L^p(0,T; L^q(\R^{3} ))$ satisfying $ \frac{2}{p}+…
We consider the steady-state Boussinesq system in the whole three-dimensional space, with the action of external forces and the gravitational acceleration. First, for $3<p\leq +\infty$ we prove the existence of weak $L^p$-solutions.…
The purpose of this paper is to establish the regularity the weak solutions for a nonlinear biharmonic equation.
In this paper we consider three-dimensional incompressible magnetohydrodynamics equations. By using interpolation inequalities in anisotropic Lebesgue space, we provide regularity criteria involving the velocity or alternatively involving…
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…
The main issue addressed in this paper concerns an extension of a result by Z. Zhang who proved, in the context of the homogeneous Besov space $\dot{B}_{\infty ,\infty }^{-1}(\mathbb{R}% ^{3})$, that, if the solution of the Boussinesq…
In this article, we study regularity criteria for the 3D micropolar fluid equations in terms of one partial derivative of the velocity. It is proved that if \begin{equation*}…
The Boussingesq equations was introduced in understanding the coupling nature of the thermodynamics and the fluid dynamics. We show the existence of continuous periodic weak solutions of the Boussinesq equations which satisfies the…
Consider the time-periodic viscous incompressible fluid flow past a body with non-zero velocity at infinity. This article gives sufficient conditions such that weak solutions to this problem are smooth. Since time-periodic solutions do not…
In this paper, we study the averaging principle for 2D Boussinesq equations with non-Lipschitz Poisson jump noise. Precisely, we will first explore the well-posedness, regularity estimates and tightness of the vorticity variable. Then, we…
In this paper, we consider the regularity criterion for 3D incompressible Navier-Stokes equations in terms of one directional derivative of the velocity in anisotropic Lebesgue spaces. More precisely, it is proved that u becomes a regular…
In this paper, we prove that the Leray weak solution $u : \mathbb{R}^3\times (0, T)\rightarrow\mathbb{R}^3 $ of the Navier-Stokes equations is regular in $\mathbb{R}^3\times (0,T)$ under the scaling invariant Serrin condition imposed on one…
This paper examines the question for global regularity for the Boussinesq equation with critical fractional dissipation. The main result states that the system admits global regular solutions for all (reasonably) smooth and decaying data,…