# Global Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation

@article{Regmi2016GlobalRF, title={Global Regularity for the 2D Magneto-Micropolar Equations with Partial Dissipation}, author={Dipendra Regmi and Jiahong Wu}, journal={The Journal of Men's Studies}, year={2016}, volume={49}, pages={169-194} }

This paper studies the global existence and regularity of classical solutions to the 2D incompressible magneto-micropolar equations with partial dissipation. The magneto-micropolar equations model the motion of electrically conducting micropo- lar fluids in the presence of a magnetic field. When there is only partial dissipation, the global regularity problem can be quite difficult. We are able to single out three special partial dissipation cases and establish the global regularity for each…

## 29 Citations

### Global regularity and decay estimates for 2D magneto-micropolar equations with partial dissipation

- MathematicsZeitschrift für angewandte Mathematik und Physik
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This paper examines the global regularity problem and decay estimates for two classes of two-dimensional (2D) magneto-micropolar equations with partial dissipation. By fully exploiting the special…

### Global regularity for the 2D magneto-micropolar equations with partial and fractional dissipation

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### Global regularity for 2D magneto-micropolar equations with only micro-rotational velocity dissipation and magnetic diffusion

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### On two-dimensional incompressible magneto-micropolar system with mixed partial viscosity

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### GLOBAL REGULARITY CRITERIA FOR 2D MICROPOLAR EQUATIONS WITH PARTIAL DISSIPATIONS

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This article addresses the global regularity (in time) issue of two dimensional incompressible micropolar equations with various partial dissipations. Micropolar fluids represent a class of fluids…

### The 2D magneto‐micropolar equations with partial dissipation

- MathematicsMathematical Methods in the Applied Sciences
- 2019

We study the global existence and regularity of classical solutions to the 2D incompressible magneto‐micropolar equations with partial dissipation. We establish the global regularity for one partial…

### Global regularity for the 2D magneto‐micropolar system with partial and fractional dissipation

- MathematicsMathematical Methods in the Applied Sciences
- 2019

This paper focuses on the 2D incompressible magneto‐micropolar sysytem with the kinematic dissipation given by the fractional operator (−Δ)α, the magnetic diffusion by the fractional operator (−Δ)β…

### Existence and Time Decay for Global Small Solution of 2D Generalized Magneto-Micropolar Equations

- MathematicsActa Applicandae Mathematicae
- 2021

This paper is concerned with the 2D magneto-micropolar equations with linear velocity damping and partial magnetic diffusion. We first examine that this system possesses a unique global smooth…

### Large time decay of solutions for the 3D magneto-micropolar equations

- MathematicsNonlinear Analysis: Real World Applications
- 2018

## References

SHOWING 1-10 OF 32 REFERENCES

### The 2D Incompressible Magnetohydrodynamics Equations with only Magnetic Diffusion

- MathematicsSIAM J. Math. Anal.
- 2014

This result significantly improves previous work and brings the resolution of the well-known global regularity problem on the 2D MHD equations with standard Laplacian magnetic diffusion, namely, the case when $\beta=1$.

### Global regularity for the 2D MHD equations with mixed partial dissipation and magnetic diffusion

- Mathematics
- 2009

### BKM's Criterion and Global Weak Solutions for Magnetohydrodynamics with Zero Viscosity

- Mathematics
- 2009

In this paper we derive a criterion for the breakdown of classical solutions to the incompressible magnetohydrodynamic equations with zero viscosity and positive resistivity in $\mathbb{R}^3$. This…

### Global Regularity for a Class of Generalized Magnetohydrodynamic Equations

- Mathematics
- 2011

It remains unknown whether or not smooth solutions of the 3D incompressible MHD equations can develop finite-time singularities. One major difficulty is due to the fact that the dissipation given by…

### Global regularity of 2D generalized MHD equations with magnetic diffusion

- Mathematics
- 2015

This paper is concerned with the global regularity of the 2D (two-dimensional) generalized magnetohydrodynamic equations with only magnetic diffusion $${\Lambda^{2\beta} b}$$Λ2βb . It is proved that…

### Global regularity of the 2D magnetic micropolar fluid flows with mixed partial viscosity

- MathematicsComput. Math. Appl.
- 2015

### Global Existence for Two Dimensional Incompressible Magnetohydrodynamic Flows with Zero Magnetic Diffusivity

- Mathematics, Physics
- 2014

The existence of global-in-time classical solutions to the Cauchy problem of incompressible Magnetohydrodynamic flows with zero magnetic diffusivity is considered in two dimensions. The linearization…