Model equations and structures formation for the media with memory

TL;DR

This paper introduces new models for media with memory, including hyperbolic Navier-Stokes modifications and low-dimensional dynamical models, demonstrating structure formation, chaos, and potential applications to solar phenomena.

Contribution

It presents novel hyperbolic and low-dimensional models for media with memory, showing their ability to simulate structure formation and chaotic behavior.

Findings

Small- and large-scale structures form in models with memory

Chaotic solutions emerge in the models

Potential applications to solar burst processes

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.