Global Classical Solutions to the 2D Compressible MHD Equations with Large Data and Vacuum

2014/09/19 by Yu Mei, Mei, Yu
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.1409.5665

openalex publication_date 2014/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the global well-posedness of classical solutions to the 2D compressible MHD equations with large initial data and vacuum. With the assumption μ=const. and λ=ρ^β,~β>1 (Vaǐgant-Kazhikhov Model) for the viscosity coefficients, the global existence and uniqueness of classical solutions to the initial value problem is established on the torus \mathbbT² and the whole space ℝ² (with vacuum or non-vacuum far fields). These results generalize the previous ones for the Vaǐgant-Kazhikhov model of compressible Navier-Stokes.

Citations

• Global classical solution to the Cauchy problem of 2D baratropic compressible Navier-Stokes system with large initial data
• Global classical solutions to the two-dimensional compressible Navier-Stokes equations in ℝ²
• Existence and Blowup Behavior of Global Strong Solutions to the Two-Dimensional Baratropic Compressible Navier-Stokes System with Vacuum and Large Initial Data
• On commutators of singular integrals and bilinear singular integrals

Related

• Global well-posedness for the two dimensional compressible MHD equations with large data
• Global well-posedness of 2D compressible Navier-Stokes equations with large data and vacuum
• Global classical solutions to the two-dimensional compressible Navier-Stokes equations in ℝ²
• Global Strong and Weak Solutions to the Initial-boundary-value Problem of 2D Compressible MHD System with Large Initial Data and Vacuum
• Global Well-Posedness of Classical Solutions to the Cauchy problem of Two-Dimensional Baratropic Compressible Navier-Stokes System with Vacuum and Large Initial Data