Forward self-similar solutions to the MHD equations: existence and pointwise estimates

2024/04/03 by Yifan Yang, Yang, Yifan
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Gas Dynamics and Kinetic Theory #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2404.02601

openalex publication_date 2024/04/03 · openalex created_date 2024/04/06 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the forward self-similar solutions to the three-dimensional Magnetohydrodynamic equations (MHD equations) in the whole space. By employing the Leray-Schauder theorem and blow-up argument, we construct a global-time forward self-similar solutions, which is smooth in \R³×(0,∞). Furthermore, by investigating the regularity of the weak solutions to the corresponding Leray system in the weighted Sobolev space, we can derive the pointwise estimate for the forward self-similar solution.

Related

• Forward self-similar solutions of the MHD-boussinesq system with newtonian gravitational field
• Existence of infinite-energy and discretely self-similar global weak solutions for 3D MHD equations
• Self-similar singularities for electron MHD
• Axisymmetric self-similar solutions to the MHD equations without magnetic diffusion
• Axisymmetric self-similar solutions to the MHD equations