In this paper our aim is to derive an upper bound on the dimension of the attractor of the family of processes associated to the Navier-Stokes equations with nonhomogeneous boundary conditions depending on time. We consider two-dimensional flows with prescribed quasiperiodic (in time) tangential velocity at the boundary, and obtain an upper bound which is polynomial with respect to the viscosity.
A. Miranville and X. Wang, "Attractors for Nonautonomous Nonhomogeneous Navier-Stokes Equations," Nonlinearity, vol. 10, no. 5, pp. 1047 - 1061, IOP Publishing; London Mathematical Society, Sep 1997.
The definitive version is available at https://doi.org/10.1088/0951-7715/10/5/003
Mathematics and Statistics
International Standard Serial Number (ISSN)
Article - Journal
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01 Sep 1997