3D Micropolar Fluid Research Articles

Thermal Performance of Cattaneo-Christov Heat Flux Model on 3D Micropolar Fluid with Motile Microbes Across a Permeable Surface

Thermal Performance of Cattaneo-Christov Heat Flux Model on 3D Micropolar Fluid with Motile Microbes Across a Permeable Surface

Eigenvalue Regularity Criteria of the Three-Dimensional Micropolar Fluid Equations

In this paper, we consider several improved regularity criteria to the 3D micropolar fluid equations. In particular, we prove regularity criteria that only require control of the middle eigenvalue of strain tensor in critical Besov spaces, which can be regarded as improvement and extension of results very recently obtained.

Global regularity for the 3D micropolar fluid flows

The aim of this note is to establish the global regularity of classical solutions of the 3D micropolar fluid equations for a family of large initial data with finite energy.

Blow-up criteria of strong solutions to the 3D micropolar fluid equations with partial viscosities

This paper studies the blow-up criteria of strong solutions to the 3-dimensional incompressible micropolar fluid equations with partial viscosities. Two blow-up criteria are given to the local-in-time strong solution. The proof is based on energy estimates and harmonic analysis methods.

A new regularity criterion of weak solutions to the 3D micropolar fluid flows in terms of the pressure

In this study, we establish a new regularity criterion of weak solutions to the three-dimensional micropolar fluid flows by imposing a critical growth condition on the pressure field.

A regularity criterion for three-dimensional micropolar fluid equations in Besov spaces of negative regular indices

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 $$\begin{aligned} \int ^{T}_{0}\Vert \partial _{3}u\Vert ^{\frac{2}{1-r}}_{\dot{B}^{-r}_{\infty ,\infty }} dt<\infty \quad \text {with} \quad 0< r<1, \end{aligned}$$ then, the solutions of the micropolar fluid equations actually are smooth on (0, T). This improves and extends many previous results.

Blow-up criterion for the 3D micropolar fluid equations

Blow-up criterion for the 3D micropolar fluid equations

Optimal control problem for 3D micropolar fluid equations

Optimal control problem for 3D micropolar fluid equations

The anisotropic integrability logarithmic regularity criterion to the 3D micropolar fluid equations

The aim of this paper is to establish the regularity criterion of weak solutions to the 3D micropolar fluid equations by one directional derivative of the pressure in anisotropic Lebesgue spaces. We improve the regularity criterion for weak solutions previously given by Jia, Zhang and Dong in [ 21 ].

Inclined Lorentz force effects on 3D micropolar fluid flow due to a stretchable rotating disks with higher order chemical reaction

The present work deals with an inclined magnetohydrodynamic flow of a micropolar fluid occurring between two stretchable disks rotating co-axially at a constant distance apart by taking into account higher order chemical reaction effects. Using similarity variables the Navier–Stokes equations, which represent the momentum, microrotation, energy, and concentration, are transformed into ordinary differential equations. The transformed conservation equations are solved numerically by using the Nachtsheim–Swigert shooting iteration technique along with sixth-order Runge–Kutta integration scheme. The influence of governing parameters are shown graphically and discussed. It was observed that an increase in the aligned angle strengthens the applied magnetic field and decreases the momentum boundary layer profiles of the micropolar fluid flow. Heat transfer rate reduces for larger values of chemical reaction Cr for both n = 1 and n = 2.

Regularity Criterion for the 3D Micropolar Fluid Equations in Terms of Pressure

In this paper, we consider the regularity of weak solutions to the 3D incompressible micropolar fluid equations. It is proved that if the one directional derivative of the pressure, say $$\partial _{3}P$$ , satisfies $$\begin{aligned} \partial _{3}P \in L^{\beta }(0,T;L^{\alpha }(\mathbb {R}^{3})) \quad \text { with } \frac{2}{\beta }+\frac{3}{\alpha }\le 2, \frac{3}{2}\le \alpha <\infty , \end{aligned}$$ then the corresponding weak solution $$(u,\omega )$$ is regular on [0, T].

A Regularity Criterion in Terms of Direction of Vorticity to the 3D Micropolar-fluid Equations

A Regularity Criterion in Terms of Direction of Vorticity to the 3D Micropolar-fluid Equations

A regularity criterion for 3D micropolar fluid flows in terms of one partial derivative of the velocity

In this work, we prove a regularity criterion for micropolar fluid flows in terms of the one partial derivative of the velocity in Morrey-Campanato space.

Logarithmically Improved Regularity Criterion for the 3D Micropolar Fluid Equations

We study the regularity of weak solutions to the incompressible micropolar fluid equations. We obtain an improved regularity criterion in terms of vorticity of velocity in Besov space. It is proved that if the vorticity field satisfies ∫0T∇×uB˙∞,∞0/1+log1+∇×uB˙∞,∞0dt&lt;∞ then the strong solution can be smoothly extended after time T.

Existence of solutions for the 3D-micropolar fluid system with initial data in Besov–Morrey spaces

In this paper, we show a local-in-time existence result for the 3D micropolar fluid system in the framework of Besov–Morrey spaces. The initial data class is larger than the previous ones and contains strongly singular functions and measures.

A New Pressure Regularity Criterion of the Three-Dimensional Micropolar Fluid Equations

This paper concerns the regularity criterion of the weak solutions to the three-dimensional (3D) micropolar fluid equations in terms of the pressure. It is proved that if one of the partial derivatives of pressure satisfies with , then the weak solution of the micropolar fluid equations becomes regular on .

Global mild solutions of the micropolar fluid system in critical spaces

We prove the global in time existence of a small solution for the 3D micropolar fluid system in critical Fourier&#8211;Herz spaces by using the Fourier localization method and Littlewood&#8211;Paley theory.

A logarithmically improved blow-up criterion for smooth solutions to the 3D micropolar fluid equations

In this paper, the Cauchy problem for the 3D micropolar fluid equations is investigated. A new logarithmically improved blow-up criterion for the 3D micropolar fluid equations in an appropriate homogeneous Besov space is established.

Logarithmically improved regularity criteria for the micropolar fluid equations

We discuss the 3D incompressible micropolar fluid equations, and give logarithmically improved regularity criteria in terms of both the velocity field and the pressure in Morrey&#8211;Campanato spaces, BMO spaces and Besov spaces.

Logarithmically Improved Blow up Criterion for Smooths Solution to the 3D Micropolar Fluid Equations

Blow‐up criteria of smooth solutions for the 3D micropolar fluid equations are investigated. Logarithmically improved blow‐up criteria are established in the Morrey‐Campanto space.