# Forward Discretely Self-Similar Solutions of the MHD Equations and the Viscoelastic Navier-Stokes Equations with Damping

## TL;DR

This paper establishes the existence of forward discretely self-similar solutions for the MHD and viscoelastic Navier-Stokes equations with damping, even with large initial data in weak L^3 spaces.

## Contribution

It introduces a method to construct self-similar solutions for these complex fluid equations with large initial data, extending previous techniques.

## Key findings

- Existence of solutions with large weak L^3 initial data.
- Application of techniques from Bradshaw and Tsai (2017).
- Construction of self-similar solutions for MHD and viscoelastic Navier-Stokes equations.

## Abstract

In this paper, we prove the existence of forward discretely self-similar solutions to the MHD equations and the viscoelastic Navier-Stokes equations with damping with large weak $L^3$ initial data. The same proving techniques are also applied to construct self-similar solutions to the MHD equations and the viscoelastic Navier-Stokes equations with damping with large weak $L^3$ initial data. This approach is based on [Z. Bradshaw and T.-P. Tsai, Ann. Henri Poincar'{e}, vol. 18, no. 3, 1095-1119, 2017].