Kelvin-Voigt Impulse Equations of Incompressible Viscoelastic Fluid Dynamics
S. N. Antontsev1, I. V. Kuznetsov1,2, S. A. Sazhenkov1,2
1Lavrentyev Institute of Hydrodynamics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk, Russia
2Altai State University, Barnaul, Russia
Keywords: impulse partial differential equations, Kelvin-Voigt fluid, convection, initial layer
Abstract
This paper describes a multidimensional initial-boundary-value problem for Kelvin-Voigt equations for a viscoelastic fluid with a nonlinear convective term and a linear impulse term, which is a regular junior term describing impulsive phenomena. The impulse term depends on an integer positive parameter n , and, as n → +∞, weakly converges to an expression that includes the Dirac delta function that simulates impulse phenomena at the initial time. It is proven that, as n → +∞ an infinitesimal initial layer associated with the Dirac delta function is formed and the family of regular weak solutions of the initial-boundary value problem converges to a strong solution of a two-scale micro- and macroscopic model.
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