Kelvin–Voigt impulse equations of incompressible viscoelastic fluid dynamics

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 $n\to+\infty$, weakly converges to an expression that includes the Dirac delta function that simulates impulse phenomena at the initial time. It is proven that, as $n\to+\infty$ 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.