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A note on the regularity of the holes for permeability property through a perforated domain for the 2D Euler equations:Dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

引用

Science China Mathematics 2019年第6期62卷 1121-1142页

作者： Christophe Lacave Chao Wang Institut Fourier Université Grenoble AlpesCNRS School of Mathematical Sciences Peking University

For equations of order two with the Dirichlet boundary condition, as the Laplace problem, the Stokes and the Navier-Stokes systems, perforated domains were only studied when the distance between the holes d_ε is equal to or much larger than the size of the holes ε. Such a diluted porous medium is interesting because it contains some cases where we have a non-negligible effect on the solution when(ε, d_ε) →(0, 0).Smaller distances were avoided for mathematical reasons and for these large distances, the geometry of the holes does not affect or rarely affect the asymptotic result. Very recently, it was shown for the 2D-Euler equations that a porous medium is non-negligible only for inter-holes distances much smaller than the sizes of the *** this result, the boundary regularity of holes plays a crucial role, and the permeability criterion depends on the geometry of the lateral boundary. In this paper, we relax slightly the regularity condition, allowing a corner, and we note that a line of irregular obstacles cannot slow down a perfect fluid in any regime such thatε ln d_ε→ 0.

关键词： ideal fluids homogenization in perforated domains shrinking obstacles and the porous medium domains with corners

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