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arXiv 0904.2422math.AP
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三维Navier-斯托克斯方程的高阶导数估计

Higher derivatives estimate for the 3D Navier-Stokes equation

Alexis F Vasseur

摘要:

本文引入了一类基于能量耗散的非线性空间族。这个族将能量空间(包含Navier-斯托克斯方程的弱解)连接到临界空间(通过Navier-斯托克斯方程的正则标度不变)。这个族被用来得到三维Navier-斯托克斯方程解的高阶导数的一致估计。这些估计是统一的,直到可能的爆炸时间。证明使用了爆破技术。由于方程中传输部分的伽利略不变性,可以通过这种方法获得估计值。

英文摘要:

In this article, a non linear family of spaces, based on the energy dissipation, is introduced. This family bridges an energy space (containing weak solutions to Navier-Stokes equation) to a critical space (invariant through the canonical scaling of the Navier-Stokes equation). This family is used to get uniform estimates on higher derivatives to solutions to the 3D Navier-Stokes equations. Those estimates are uniform, up to the possible blowing-up time. The proof uses blow-up techniques. Estimates can be obtained by this means thanks to the galilean invariance of the transport part of the equation.

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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