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arXiv · 1607.07643

Global well-posedness for the two-dimensional Maxwell-Navier-Stokes equations

Changxing Miao·Xiaoxin Zheng
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Abstract

In this paper, we investigate Cauchy problem of the two-dimensional full Maxwell-Navier-Stokes system, and prove the global-in-time existence and uniqueness of solution in the borderline space which is very close to $L^2$-energy space by developing the new estimate of $\sup_{j\in\mathbb Z} 2^{2j} \int_0^t \sum_{k\in\mathbb{Z}^2} \big\| \sqrt{\phi_{i,k}} u(\tau) \big\|^2_{L^2(\mathbb{R}^2)} \text{d}\tau < \infty$. This solves the open problem in the framework of borderline space purposed by Masmoudi in \cite{Masmoudi-10}.

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Changxing Miao, Xiaoxin Zheng. 2016-07-26. Global well-posedness for the two-dimensional Maxwell-Navier-Stokes equations. https://arxiv.org/abs/1607.07643

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