# On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space

@inproceedings{Yuan2009OnRC, title={On regularity criteria for weak solutions to the micropolar fluid equations in Lorentz space}, author={Baoquan Yuan}, year={2009} }

In this paper the regularity of weak solutions and the blow-up criteria of smooth solutions to the micropolar fluid equations on three dimension space are studied in the Lorentz space $L^{p,\infty}(\mathbb{R}^3)$. We obtain that if $u\in L^q(0,T;L^{p,\infty}(\mathbb{R}^3))$ for $\frac2q+\frac3p\le 1$ with $3<p\le \infty$; or $\nabla u\in L^q(0,T;L^{p,\infty}(\mathbb{R}^3))$ for $\frac2q+\frac3p\le 2$ with $\frac32<p\le \infty$; or the pressure $P\in L^q(0,T;L^{p,\infty}(\mathbb{R}^3))$ for…

## 44 Citations

### Blow-up criteria of smooth solutions to the three-dimensional micropolar fluid equations in Besov space

- Mathematics
- 2016

In this paper, we investigate the blow-up criteria of smooth solutions and the regularity of weak solutions to the micropolar fluid
equations in three dimensions. We obtain that if
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### New Regularity Criteria Based on Pressure or Gradient of Velocity in Lorentz Spaces for the 3D Navier–Stokes Equations

- MathematicsJournal of Mathematical Fluid Mechanics
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In this paper, we derive regular criteria via pressure or gradient of velocity in Lorentz spaces to the 3D Navier–Stokes equations. It is shown that a Leray–Hopf weak solution is regular on (0, T ]…

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

- Mathematics
- 2020

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…

### On the Deformation Tensor Regularity for the Navier–Stokes Equations in Lorentz Spaces

- MathematicsBulletin of the Malaysian Mathematical Sciences Society
- 2021

This paper is concerned with the regularity criteria in terms of the middle eigenvalue of the deformation (strain) tensor $$\mathcal {D}(u)$$ D ( u ) to the 3D Navier–Stokes equations in Lorentz…

### The Gevrey analyticity and decay for the micropolar system in the critical Besov space

- MathematicsJournal of Evolution Equations
- 2021

In this paper, we are concerned with the 3-D incompressible micropolar fluid system, which is a non-Newtonian fluid exhibiting micro-rotational effects and micro-rotational inertia. We aim at…

### Regularity of Weak Solutions to the 3D Magneto-Micropolar Equations in Besov Spaces

- MathematicsActa Applicandae Mathematicae
- 2018

This paper deals with the regularity of weak solutions to the 3D magneto-micropolar fluid equations in Besov spaces. It is shown that for 0≤α≤1$0\le\alpha\le1$ if u∈L21+α(0,T;B˙∞,∞α)$u\in…

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- Mathematics
- 2019

We are concerned with compressible magneto-micropolar fluid equations (1.1)-(1.2). The global existence and large time behaviour of solutions near a constant state to the…

### A remark on the logarithmically improved regularity criterion for the micropolar fluid equations in terms of the pressure

- Mathematics
- 2011

In this paper, we study the regularity criterion of weak solutions of the three dimensional micropolar fluid flows. It is proved that if the pressure satisfies ∫0Tπ(s,.)Ḃ∞,∞−121+lne+π(s,.)L2ds<∞,…

### On regularity criteria for the three-dimensional micropolar fluid equations in the critical Morrey–Campanato space

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- 2011

### A weak-Lp Prodi-Serrin type regularity criterion for the micropolar fluid equations

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- 2016

We investigate regularity criteria for weak solutions of the micropolar fluid equations in a bounded three-dimensional domain. We show that the solution (u, w) is strong on [0, T] if either u ∈ Ls(0,…

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