论文标题
在$8π$ - 关键的质量质量阈值
On the $8π$-critical mass threshold of a Patlak-Keller-Segel-Navier-Stokes system
论文作者
论文摘要
在本文中，我们提出了一个耦合的patlak-keller-segel-navier-stokes系统，该系统具有耗散的自由能。在平面$ \ rr^2 $上，如果细胞的总质量严格小于$8π$，则在任何有限的时间内都存在经典的解决方案，并且它们的$ h^s $ -Sobolev Norms几乎均匀地界定了限制。对于径向对称的解决方案，此$8π$ - 质量阈值至关重要。在圆环$ \ mathbb {t}^2 $上，在相同的质量约束下，解决方案在时间上均匀地界定。
In this paper, we proposed a coupled Patlak-Keller-Segel-Navier-Stokes system, which has dissipative free energy. On the plane $\rr^2$, if the total mass of the cells is strictly less than $8π$, classical solutions exist for any finite time, and their $H^s$-Sobolev norms are almost uniformly bounded in time. For the radially symmetric solutions, this $8π$-mass threshold is critical. On the torus $\mathbb{T}^2$, the solutions are uniformly bounded in time under the same mass constraint.
