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arXiv 1104.3255math.AP
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三维Navier-斯托克斯方程弱解的唯一性判据

Uniqueness criterion of weak solutions for the 3D Navier-Stokes equations

Abdelhafid Younsi

摘要:

本文建立了三维Navier-斯托克斯方程弱解的一个新的唯一性结果。在奇异时间弱解不存在唯一性的假设下,证明了三维Navier-斯托克斯方程的两个弱解$u$和$v$在相同的初值下属于$L^{\frac{5}{2}}\left( 0,T;V\right) $,则得到$u=v$ .在类$L^{3}\left( 0,T;V\right) $,我们证明了$u-v\in$ $C^{0}\left( 0,T;H\right) $和$u=v\ $时$u_{0}=v_{0}$。

英文摘要:

In this paper we establish a new uniqueness result of weak solutions for the 3D Navier-Stokes equations. Under assumption that there is not uniqueness of weak solution in singular time, we prove that if two weak solutions $u$ and $v$ of 3D Navier-Stokes equations belong to $L^{\frac{5}{2}}\left( 0,T;V\right) $ with the same initial datum, then we get $u=v$. In the class $L^{3}\left( 0,T;V\right) $, we prove that $u-v\in$ $C^{0}\left( 0,T;H\right) $ and $u=v\ $when $u_{0}=v_{0}$.

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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