We consider a one-parameter family of problems, governing, for any fixed parameter, the motion of a linear viscoelastic fluid in a two-dimensional domain with periodic boundary conditions. The asymptotic behavior of each problem is analyzed, by proving the existence of the global attractor. Moreover, letting the parameter go to zero, since the memory effect disappears, we obtain a limiting problem, given by the Navier–Stokes equations. For any fixed parameter, we construct an exponential attractor. The resulting family is robust, meaning that these exponential attractors converge, in an appropriate sense, to an exponential attractor of the limiting problem.

Singular limit of equations for linear viscoelastic fluids with periodic boundary conditions / Gatti, Stefania; Vuk, E.. - In: INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS. - ISSN 0020-7462. - STAMPA. - 41(2006), pp. 518-526.

Singular limit of equations for linear viscoelastic fluids with periodic boundary conditions

GATTI, Stefania;
2006

Abstract

We consider a one-parameter family of problems, governing, for any fixed parameter, the motion of a linear viscoelastic fluid in a two-dimensional domain with periodic boundary conditions. The asymptotic behavior of each problem is analyzed, by proving the existence of the global attractor. Moreover, letting the parameter go to zero, since the memory effect disappears, we obtain a limiting problem, given by the Navier–Stokes equations. For any fixed parameter, we construct an exponential attractor. The resulting family is robust, meaning that these exponential attractors converge, in an appropriate sense, to an exponential attractor of the limiting problem.
41
518
526
Singular limit of equations for linear viscoelastic fluids with periodic boundary conditions / Gatti, Stefania; Vuk, E.. - In: INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS. - ISSN 0020-7462. - STAMPA. - 41(2006), pp. 518-526.
Gatti, Stefania; Vuk, E.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11380/453668
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