论文标题
关于运输stokes系统的一些评论
A few remarks on the transport-Stokes system
论文作者
论文摘要
我们考虑了所谓的传输stokes系统，该系统描述了粘性流中惯性悬浮液的沉积，并在整个三维空间中融合了传输方程和稳定的stoke方程。 首先，我们提出$ l^1 \ cap l^p $初始密度的全球存在和唯一性结果，其中$ p \ geq 3 $。其次，我们证明，在$ p> 3 $的情况下，描述这些解决方案轨迹的流图是相对于时间的分析。最后，我们建立了运输stokes系统的小型全球精确可控性。这些结果扩展到了运输stokes系统，分别由Yudovich在[40]中，Chemin在[2,3]和Coron和Coron和Glass [6,14]中分别为不可压缩的Euler系统获得了一些结果。
We consider the so-called transport-Stokes system which describes sedimentation of inertialess suspensions in a viscous flow and couples a transport equation and the steady Stokes equations in the full three-dimensional space. First we present a global existence and uniqueness result for $L^1 \cap L^p$ initial densities where $p \geq 3$. Secondly, we prove that, in the case where $p>3$, the flow map which describes the trajectories of these solutions is analytic with respect to time. Finally we establish the small-time global exact controllability of the transport-Stokes system. These results extend to the transport-Stokes system some results obtained for the incompressible Euler system respectively by Yudovich in [40], by Chemin in [2,3] and by Coron, and Glass, in [6,14].
