Model equations and structures formation for the 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 proposed models to the description of the burst-type processes and collapses o nthe Sun are discussed.