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

被引：0
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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.
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页码：1 / 19
页数：18
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