论文标题
关于Lorentz空间中Navier-Stokes方程的混合压力速度规则标准
On mixed pressure-velocity regularity criteria to the Navier-Stokes equations in Lorentz spaces
论文作者
论文摘要
在本文中，我们根据正式的等价关系$π\ cong | v |^2 $在Lorentz空间中的lorentz空间中定期标准$ v $，其中$π$表示流体压力和$ v $ v $ v $ v $ v $。它称为混合压力速度问题（P-V问题）。结果表明，如果$ \fπ{（e^{ - | x |^2}+| v |） $ \ om $是周期性的，我们可以通过正常常数替换$ \，$ \ e^{ - | x |^2} \ $。 Ladyzhenskaya-Prodi-Serrin（L-P-S）类型。
In this paper we derive regular criteria in Lorentz spaces for Leray-Hopf weak solutions $v$ of the three-dimensional Navier-Stokes equations based on the formal equivalence relation $π\cong|v|^2$, where $π$ denotes the fluid pressure and $v$ the fluid velocity. It is called the mixed pressure-velocity problem (the P-V problem). It is shown that if $\fπ{(e^{-|x|^2}+|v|)^θ}\in L^p(0,T;L^{q,\infty})\,,$ where $0\leqθ\leq1$ and $\f2p+\f3q=2-θ$, then $v$ is regular on $(0,T]$. Note that, if $\Om$ is periodic, we may replace $\,e^{-|x|^2} \,$ by a positive constant. This result improves a 2018 statement obtained by one of the authors. Furthermore, as an integral part of our contribution, we give an overview on the known results on the P-V problem, and also on two main techniques used by many authors to establish sufficient conditions for regularity of the so-called Ladyzhenskaya-Prodi-Serrin (L-P-S) type.
