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arXiv 1607.07643math.AP
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二维Maxwell-Navier-斯托克斯方程的整体适定性

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

Changxing Miao, Xiaoxin Zheng

摘要:

本文研究了二维Maxwell-Navier-Stokes方程组的Cauchy问题,通过对$\sup_{j\in\mathbb Z} 2^{2j} \int_0^t \sum_{k\in\mathbb{Z}^2} \big\| \sqrt{ϕ_{i,k}} u(τ) \big\|^2_{L^2(\mathbb{R}^2)} \text{d}τ< \infty$的新估计,证明了在与$L^2$ -能量空间非常接近的边界空间中解的整体存在唯一性.这解决了Masmoudi在\cite{Masmoudi-10}中提出的边界空间框架中的开放问题。

英文摘要:

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 $\sup_{j\in\mathbb Z} 2^{2j} \int_0^t \sum_{k\in\mathbb{Z}^2} \big\| \sqrt{ϕ_{i,k}} u(τ) \big\|^2_{L^2(\mathbb{R}^2)} \text{d}τ< \infty$. This solves the open problem in the framework of borderline space purposed by Masmoudi in \cite{Masmoudi-10}.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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