Long time behaviour of solutions of abstract inequalities: Applications to thermo-hydraulic and magnetohydrodynamic equations

Abstract

We study some scalar inequalities of parabolic type and we give the leading term of an asymptotic expansion as t → ∞ for solutions of thermo-hydraulic equations without external excitation. A phenomenon of resonance is pointed out. We also treat M. H. D. equations and Navier-Stokes equations on a Riemannian manifold.