Model Equations and Formation of Structures in Media with Memory

Abstract

We propose new types of models of the appearance of small- and large-scale structures in media with memory, including a hyperbolic modification of the Navier--Stokes equations and a class of dynamical low-dimensional models with memory effects. On the basis of computer modeling, the formation of the small-scale structures and collapses and the appearance of new chaotic solutions are demonstrated. Possibilities of the application of some proposedmodels to the description of the burst-type processes and collapses on the Sun are discussed.