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On the longtime behavior of a 2D hydrodynamic model for chemically reacting binary fluid mixtures
Author(s) -
Bosia Stefano,
Grasselli Maurizio,
Miranville Alain
Publication year - 2013
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2832
Subject(s) - mathematics , bounded function , compressibility , attractor , domain (mathematical analysis) , mathematical analysis , binary number , boundary value problem , cahn–hilliard equation , navier–stokes equations , boundary (topology) , convection , partial differential equation , thermodynamics , physics , arithmetic
Two dimensional diffuse interface model for a chemically reacting incompressible binary fluid in a bounded domain is considered. The corresponding evolution system consists of the Navier–Stokes equations for the (averaged) fluid velocity that are nonlinearly coupled with a convective Cahn–Hilliard–Oono type equation for the difference ψ of two fluid concentrations. The effects of a (reversible) chemical reaction is represented in the latter equation by an additional term of the form ε ( ψ − c 0 ), ε > 0. Here, c 0 is the stationary spatial average of ψ , provided that, for example, no‐slip and no‐flux boundary conditions are considered. The mass is not necessarily conserved unless the spatial average of the initial datum for ψ coincides with c 0 . When ε = 0 (i.e., no chemical reaction), the model reduces to the well‐known Cahn–Hilliard–Navier–Stokes system, which has been investigated by several authors. Here, we want to show that the global dynamic behavior of the system is robust with respect to ε . More precisely, we construct a family of exponential attractors, which is continuous with respect to ε . Copyright © 2013 John Wiley & Sons, Ltd.