论文标题
一些固定3D磁铁 - 微极流体的liouville型定理
Some Liouville-type theorems for the stationary 3D magneto-micropolar fluids
论文作者
论文摘要
在本文中，我们证明了在适当条件下在三个空间尺寸的情况下，在适当的条件下，固定磁铁 - 微极流体为固定的磁性微极流体提供了一些liouville型定理。我们首先证明，在某些生长条件下，对于电势的平均振荡，解决方案是微不足道的。然后，假设解决方案包含在$ l^p（\ mathbb {r}^3）$的情况下，则显示了类似的结果，其中$ p \ in [2,9/2）$。最后，我们显示了[1,9/4）$中$ p \的较低值的结果，并进一步假设该解决方案在无穷大处消失。
In this paper we prove some Liouville-type theorems for the stationary magneto-micropolar fluids under suitable conditions in three space dimensions. We first prove that the solutions are trivial under the assumption of certain growth conditions for the mean oscillations of the potentials. And then we show similar results assuming that the the solutions are contained in $L^p(\mathbb{R}^3)$ with $p\in[2,9/2)$. Finally we show the same result for lower values of $p\in[1,9/4)$ with the further assumption that the solutions vanish at infinity.
