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Attractors for the penalized Navier-Stokes equations. (English) Zbl 0696.35131

Summary: We consider the penalized form of the Navier-Stokes equations for a viscous incompressible fluid where the pressure and the incompressibility equation div u\(=0\) are suppressed and replaced by a penalty term in the momentum conservation equation. In the particle we study the existence of an attractor for the penalized Navier-Stokes equation, this attractor describing the long-time behaviour of the solutions. Then we let the penalty parameter tend to zero and we show how the attractors of the penalized equations approximate the attractor of the exact equations.

MSC:

35Q30 Navier-Stokes equations
76D05 Navier-Stokes equations for incompressible viscous fluids
65Z05 Applications to the sciences
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