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

Jieqiong Liu

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arXiv · 2407.15030

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

Jieqiong Liu

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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.

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Jieqiong Liu. 2024-07-21. Global well-posedness to the Cauchy problem of 2D nonhomogeneous magnetic B\'enard system with large initial data and vacuum. https://arxiv.org/abs/2407.15030

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