# Asymptotic stability of explicite infinite energy blowup solutions for three dimensional incompressible Magnetohydrodynamics equations

## TL;DR

This paper constructs and proves the asymptotic stability of explicit finite-time blowup solutions for 3D incompressible MHD equations, demonstrating the existence of stable blowup solutions with smooth initial data in a bounded domain.

## Contribution

It introduces a family of explicit finite-time blowup solutions for 3D incompressible MHD and proves their asymptotic stability in a bounded domain.

## Key findings

- Existence of explicit finite-time blowup solutions with infinite energy.
- Proof of asymptotic stability of these blowup solutions.
- Construction of stable blowup solutions with smooth initial data.

## Abstract

This paper is denoted to the study of dynamical behavior near explicit finite time blowup solutions for three dimensional incompressible Magnetohydrodynamics (MHD) equations. More precisely, we find a family of explicit finite time blowup solutions admitted smooth initial data and infinite energy in whole space $\mathbb{R}^3$. After that, we prove asymptotic stability of those explicit finite time blowup solutions for $3$D incompressible Magnetohydrodynamics equations in a smooth bounded domain with free surface $$ \Omega_{t}:=\Big\{(t,x_1,x_2,x_3):0\leq x_i\leq\sqrt{\overline{T}^*-t},\quad t\in(0,\overline{T}^*),\quad i=1,2,3\Big\}, $$ where $\overline{T}^*$ denotes the blowup time. This means we construct a family of \textbf{stable} blowup solutions for $3$D incompressible Magnetohydrodynamics equations with smooth initial data in $\Omega_t$.