KELVIN–VOIGT IMPULSIVE EQUATIONS OF INCOMPRESSIBLE VISCOELASTIC FLUID DYNAMICS

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 impulsive term, which is a regular junior term describing impulsive phenomena. The impulsive term depends on an integer positive parameter \(n\), and, as \(n\to+\infty\), weakly converges to an expression that includes the Dirac delta function that simulates impulsive phenomena at the initial time. It is proven that, as \(n\to+\infty\), 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.