Global well-posedness to the Cauchy problem of 2D nonhomogeneous magnetic B\'enard system with large initial data and vacuum

TL;DR

This paper proves the global existence and uniqueness of strong solutions for the 2D nonhomogeneous magnetic Bénard system with large initial data and vacuum, using energy estimates and interpolation inequalities.

Contribution

It establishes the first global well-posedness results for large initial data in the 2D nonhomogeneous magnetic Bénard system with vacuum.

Findings

Global existence and uniqueness of strong solutions

Applicable to large initial data with vacuum

Method relies on energy estimates and interpolation inequalities

Abstract

This paper establishes the global well-posedness of strong solutions to the nonhomogeneous magnetic B\'enard system with positive density at infinity in the whole space $\mathbb{R}^2$. More precisely, we obtain the global existence and uniqueness of strong solutions for general large initial data. Our method relies on dedicate energy estimates and a logarithmic interpolation inequality.