论文标题
在随机穿孔域中Stokes方程均质中压力的收敛性
Convergence of the pressure in the homogenization of the Stokes equations in randomly perforated domains
论文作者
论文摘要
我们认为，在有界域中不可压缩的Stokes方程的Brinkman方程的均匀化，该域被随机的小球形孔的随机收集所用。 [A. Giunti和R.M. Höfer，在几乎最小的假设上，在孔的大小上，stokes方程的均匀化，其中已经建立了流体速度场朝向Brinkman方程溶液的收敛性。在目前，我们考虑了与穿孔域中Stokes方程溶液相关的压力。我们证明，可以在孔内部扩展这种压力，并在渐近可忽略的谐波容量区域中稍微修改它，从而使其弱收敛到与Brinkman方程溶液相关的压力。
We consider the homogenization to the Brinkman equations for the incompressible Stokes equations in a bounded domain which is perforated by a random collection of small spherical holes. This problem has been studied by the same authors in [A. Giunti and R.M. Höfer, Homogenization for the Stokes equations in randomly perforated domains under almost minimal assumptions on the size of the holes] where convergence of the fluid velocity field towards the solution of the Brinkman equations has been established. In the present we consider the pressure associated to the solution of the Stokes equations in the perforated domain. We prove that it is possible to extend this pressure inside the holes and slightly modify it in a region of asymptotically negligible harmonic capacity such that it weakly converges to the pressure associated with the solution of the Brinkman equations.
