Exponential attractors for nonautonomous partially dissipative equations. (English) Zbl 1012.35010

Galusinski, C.; Hnid, M.; Miranville, A.

Differ. Integral Equ. 12, No. 1, 1-22 (1999).

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.

Reviewer: Ivan Straškraba (Praha)

MSC:

35B41	Attractors
35Q30	Navier-Stokes equations
35B40	Asymptotic behavior of solutions to PDEs
35B45	A priori estimates in context of PDEs
47J35	Nonlinear evolution equations

Keywords:

quasiperiodic in time coefficients; 2D slightly compressible Navier-Stokes equations