Extension criterion via two-components of vorticity on strong solutions to the 3 D Navier-Stokes equations
Extension criterion via two-components of vorticity on strong solutions to the 3 D Navier-Stokes equations
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DOI：
10.1007/s00209-003-0576-1
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发表时间：
2004
影响因子：
0.8
通讯作者：
H. Kozono;N. Yatsu
中科院分区：
文献类型：
--
作者：
H. Kozono;N. Yatsu
我们将表明，只有两个组成部分的涡度发挥重要作用，以确定可能性的时间间隔延长的局部强解的Navier-Stokes方程。然后，我们将应用我们的扩张定理，由于Serrin和Beirão da Veiga弱解的正则性准则。Chae-Choe仅通过涡度的两个分量证明了与Beirão da Veiga相同的准则。我们处理他们排除的关键情况。我们的判据可以看作是Beal-Kato-Majda的结果从mL ∞到BMO的推广。
We shall show that only two components of vorticity play an essential role to determine possibility of extension of the time interval for the local strong solution to the Navier-Stokes equations. Then we shall apply our extension theorem to regularity criterion on weak solutions due to Serrin and Beirão da Veiga. Chae–Choe proved the same criterion as Beirão da Veiga only by means of the two-components of vorticity. We deal with the critical case which they excluded. Our criterion may be regarded as the generalization of the result of Beal-Kato-Majda fromL∞toBMO.