相关论文: A Weighted Regularity Criterion for Suitable Weak …
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…
In this paper, we continue our work in [15] to derive {\epsilon}-regularity criteria at one scale without pressure for suitable weak solutions to the Navier-Stokes equations. We establish a $\varepsilon$-regularity criterion below of…
We present a weighted version of the Caffarelli-Kohn-Nirenberg inequality in the framework of variable exponents. The combination of this inequality with a variant of the fountain theorem, yields the existence of infinitely many solutions…
In this paper, we prove that a weak solution of the Cauchy problem for 3D unsteady flows of a generalized Newtonian fluid becomes a strong solution for $\frac{5}{3} <p<\frac{11}{5} $ provided that the gradient of velocity $\nabla…
A class of sufficient conditions of local regularity for suitable weak solutions to the nonstationary three-dimensional Navier-Stokes equations are discussed. The corresponding results are formulated in terms of functionals which are…
In this paper, we study regularity of weak solutions to the incompressible Boussinesq equations in $\mathbb{R}^{3}\times (0,T)$. The main goal is to establish the regularity criterion in terms of one velocity component and the gradient of…
Methods for simple and effective determination of reological parameters of non-Newtonian liquids are proposed
The goal of this paper is to propose a theoretical framework to study homogeneous and isotropic turbulence in a viscoelastic fluid, regarded as a perturbation of a Newtonian incompressible fluid, where the fluid relaxation time, or else the…
In this paper, we study the problem of energy equality for weak solutions of the 3D incompressible non-Newtonian fluid equations with initial value conditions. We derive new sufficient conditions via Sobolev multiplier spaces that guarantee…
We prove a sufficient conditions of local regularity of suitable weak solutions to the MHD system for the point from $C^3$-smooth part of the boundary. Our conditions are the generalizing of the Caffarelli--Kohn--Nirenberg theorem for…
This paper is concerned with regular flows of incompressible weakly viscoelastic fluids which obey a differential constitutive law of Oldroyd type. We study the newtonian limit for weakly viscoelastic fluid flows in $\R^N$ or $\T^N$ for…
We are concerned with the energy equality for weak solutions to Newtonian and non-Newtonian incompressible fluids. In particular, the results obtained for non-Newtonian fluids, after restriction to the Newtonian case, equal or improve the…
The object of this paper is twofold. Firstly, we study a class of generalized Newtonian fluid related to "power law ". For the corresponding non-Newtonian Navier-Stokes problems, the existence of a weak and periodic solutions is proved in…
A study of regularity estimate for weak solution to generalized stationary Stokes-type systems involving $p$-Laplacian is offered. The governing systems of equations are based on steady incompressible flow of a Newtonian fluids. This paper…
This work focuses on the 3D incompressible magnetohydrodynamic (MHD) equations with mixed pressure-velocity-magnetic field in view of Lorentz spaces. Our main result shows the weak solution is regular, provided that $${\frac{\pi }{\left(…
In this paper, we derive regular criteria via pressure or gradient of the velocity in Lorentz spaces to the 3D Navier-Stokes equations. It is shown that a Leray-Hopf weak solution is regular on $(0,T]$ provided that either the norm…
We investigate multidimensional model for incompressible non-Newtonian fluids. Using method of energy estimates we prove the property of finite speed of propagations of the solution support for this problem. We find sharp bounds of the…
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 purpose of this note is to give a complete proof of a $C^{0,\alpha}$ regularity result for the pressure for weak solutions of the two-dimensional "incompressible Euler equations" when the fluid velocity enjoys the same type of…
We consider a non-Newtonian fluid flow in a thin domain with thickness $\eta_\varepsilon$ and an oscillating top boundary of period $\varepsilon$. The flow is described by the 3D incompressible Navier-Stokes system with a nonlinear…