Long time behavior for partly dissipative equations: the slightly compressible 2D-Navier–Stokes equations

Article type: Research Article

Authors: Ghidaglia, J.M. | Temam, R.

Affiliations: Laboratoire d'Analyse Numérique, C.N.R.S. et Université de Paris-Sud, 91405 Orsay Cedex, France

Abstract: It is known that for dissipative evolution equations, the long time behavior of the solutions is generally described by a compact attractor to which all solutions converge, while such a result is not true for conservative equations of Hamiltonian type. In this paper we consider a partly dissipative system corresponding to the equations of slightly compressible fluids and investigate the long time behavior of their solutions. Despite the lack of compactness and smoothing effect for the pressure variable, the existence of a global attractor is shown and its fractal dimension is estimated.

DOI: 10.3233/ASY-1988-1104

Journal: Asymptotic Analysis, vol. 1, no. 1, pp. 23-49, 1988