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Long time behavior for partly dissipative equations: The slightly compressible 2D-Navier-Stokes equations. (English) Zbl 0657.76029

It is considered a partly dissipative system of Navier-Stokes type, but with a very small compressibility. This system agrees with a Navier- Stokes system when the perturbation parameter (in the continuity equation) tends to zero. Some existence results are proved for several types of boundary conditions. The main part of the paper is to show the existence of an universal attractor of the studied system; it is proved also that all functional invariant sets (bounded in \(H^{-1})\) have finite fractal and Hausdorff dimensions. Some results from previous papers are used, especially those from the article of P. Constantin, C. Foias and the second author, Mem. Amer. Math. Soc. 314, 67 p. (1985; Zbl 0567.35070).
Reviewer: G.Pasa

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
35Q30 Navier-Stokes equations

Citations:

Zbl 0567.35070
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