Abstract.
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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Accepted 11 July 1996
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Ziane, M. On the Two-Dimensional Navier—Stokes Equations with the Free Boundary Condition . Appl Math Optim 38, 1–19 (1998). https://doi.org/10.1007/s002459900079
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DOI: https://doi.org/10.1007/s002459900079