论文标题
navier-在总空间中规定规律性标准
Navier--Stokes regularity criteria in sum spaces
论文作者
论文摘要
在本文中，我们将考虑与混合Lebesgue Sum Spaces中的Navier方程的规律性标准。特别是，我们将证明只需要控制应变矩阵的第二特征值的速度，涡度或正征性速度的正分部分的规律性标准。这是向前迈出的重要一步，因为每个总和规律性标准涵盖了一个估计中的整个规模临界规则标准。为了证明这一点，我们还将证明在混合Lebesgue空间家族中具有尺度不变性的混合空间的新包容性和不平等，这也具有独立的兴趣。
In this paper, we will consider regularity criteria for the Navier--Stokes equation in mixed Lebesgue sum spaces. In particular, we will prove regularity criteria that only require control of the velocity, vorticity, or the positive part of the second eigenvalue of the strain matrix, in the sum space of two scale critical spaces. This represents a significant step forward, because each sum space regularity criterion covers a whole family of scale critical regularity criteria in a single estimate. In order to show this, we will also prove a new inclusion and inequality for sum spaces in families of mixed Lebesgue spaces with a scale invariance that is also of independent interest.
