Abstract
AbstractWe investigate the dynamics of bodies with vector-type microstructure. We consider linear constitutive relations and a nonlinear coupling between macroscopic and microscopic motions, determined by gyroscopic-type inertia. Based on an existence result obtained in the presence of viscous-type stress components, we determine the existence of a global attractor; its weak nature derives from the lack of uniqueness determined by the nonlinear coupling.
Funder
Università degli Studi di Firenze
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,General Physics and Astronomy,General Mathematics
Reference20 articles.
1. Bessaih, H., Flandoli, F.: Weak attractor for a dissipative Euler equation. J. Dyn. Differ. Equ. 12, 713–732 (2000)
2. Bisconti, L., Catania, D.: Remarks on global attractors for the 3D Navier–Stokes equations with horizontal filtering. Discrete Contin. Dyn. Syst. Ser. B 20, 59–75 (2015)
3. Bisconti, L., Mariano, P.M.: Existence results in the linear dynamics of quasicrystals with phason diffusion and nonlinear gyroscopic effects. Multiscale Model. Simul. 15, 745–767 (2017)
4. Capriz, G.: Continua with Microstructure. Springer, Heidelberg (1989)
5. Capriz, G., Giovine, P.: On microstructural inertia. Math. Models Methods Appl. Sci. 7, 211–216 (1997)