On the Two-Dimensional Navier—Stokes Equations with the Free Boundary Condition

被引：0

作者：

M. Ziane

机构：

[1] Department of Mathematics,

[2] and the Institute for Scientific Computing and Applied Mathematics,undefined

[3] Indiana University,undefined

[4] Bloomington,undefined

[5] IN 47405,undefined

[6] USA ziane@leland.stanford.edu ,undefined

来源：

Applied Mathematics and Optimization | 1998年 / 38卷

关键词：

Key words. Navier—Stokes equations, Trilinear form, Global attractors, Hausdorff and fractal dimensions, Grashof number, Elongated domains. AMS Classification. 34C35, 35Q30, 76D05.;

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摘要：

In this article we consider the two-dimensional Navier—Stokes equations with free boundary condition (open surface), and derive a number of different results: a new orthogonal property for the nonlinear term, improved a priori estimates on the solution, an upper bound on the dimension of the attractor which agrees with the conventional theory of turbulence; finally, for elongated rectangular domains, an improved Lieb—Thirring (collective Sobolev) inequality leads to an upper bound on the dimension of the attractor which might be optimal.

引用

页码：1 / 19

页数：18