SLIGHTLY COMPRESSIBLE 2D NAVIER-STOKESEQUATIONS REVISITED

摘要

We consider the slightly compressible 2D Navier-Stokes equations which is a perturbation of the incompressible Navier-Stokes equations. We construct a family of exponential attractors M_∈ which converge as the parameter of perturbation ∈ > 0 goes to 0. More precisely, we show that the exponential attractors M∈are upper and lower-semicontinuous at ∈ = 0. Up to now, only the lower semicontinuity result was known. To prove the upper semicontinuity result a proper control of the difference of the solutions to the perturbed and unperturbed problems is needed. We do this by working on a suitable absorbing set.