Navier边界条件下湖方程的边界层问题  

Boundary Layers for the Viscous Lake Equations with Navier Boundary Conditions

作　　者：蔡晓静[1,2] 酒全森[3] 牛冬娟[3] 

机构地区：[1]北京工商大学理学院数学系,北京100048 [2]北京工业大学应用数理学院,北京100124 [3]首都师范大学数学科学学院,北京100048

出　　处：《数学学报（中文版）》2012年第5期929-946,共18页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目(11171229);北京市教委项目

摘　　要：考虑光滑区域上二维粘性湖方程在Navier边界条件下的无粘极限问题,证明了具有Navier边界条件粘性湖方程的边界层在Sobolev空间中是非线性稳定的,验证了具有较弱强度的边界层的渐近展开的合理性.t We consider the inviscid limit of the two-dimensional viscous lake equations when the Navier slip conditions are prescribed on the impermeable boundaries of the general regular domains. Our results show that the boundary layer of the viscous lake equations with Navier boundary is always nonlinearly stable in some Sobolev spacesand we justify an asymptotic expansion which involves a weak amplitude boundary layer, with the same thickness as in asymptotic theory and a linear behavior.

关 键 词：粘性湖方程 Navier边界条件 湖方程 粘性消失极限 

分 类 号：O175.2[理学—数学] O175.8[理学—基础数学]