Navier-Stokes流近临界指标的均匀化

Homogenization of the Navier-Stokes flow near the critical index

主要研究了在三维的多孔介质中近临界指标的定常Navier-Stokes流的均匀化.采用渐近展开的方法,得到了当孔径充分小时,流体的运动状态满足"双压力均匀化方程",同时也利用构造的辅助问题的解,得到双压力方程解的表述形式.

Homogenization of the Navier-Stokes flow near the critical index in porous medium in R^3 is considered in this paper. The ＂double pressures effective equations＂ is obtained when ε,the size of the pores tends to zero by using the formal asymptotic expansion. The solution to this effective model is given by using an auxiliary problem.