Exponential attractors for nonautonomous partially dissipative equations (Q1854055)

The following problem in a Hilbert space \(H\) is considered: \(u'(t)={\mathcal G} (\alpha ,t,u(t)),\) \(t>\tau ,\) \(u(\tau)=u_\tau \in H,\) where \(\tau \in \mathbb{R}\), \(\alpha =(\alpha _1,\dots ,\alpha _k)\) with \(\alpha _i\) rationally independent and \({\mathcal G}(\omega _1,\dots ,\omega _k,\cdot)\) is \(2\pi \)-periodic in each \(\omega _i.\) An abstract scheme leading to existence of the exponential attractor for the above evolution process is formulated and then applied to the slightly compressible 2D Navier-Stokes equations for which the uniform exponential attractor is constructed.