We give some regularity criterion (of a weak\(-L^{p}\) Serrin type) of a weak solution to the 3D Navier–Stokes equations in a bounded domain \(\Omega \subset \mathbb {R}^3\) with a smooth boundary. In particular, in case of the half space, we give a regularity condition of a weak solution with respect to a tangential component of the velocity flow vector.

中文翻译：

---

域中3D Navier–Stokes方程弱解的一些正则性准则

我们给予一定的规律性标准（a弱的\（ - L ^ {P} \） Serrin类型）的稀溶液到3D Navier-Stokes方程中的有界区域的\（\欧米茄\子集\ mathbb {R} ^ 3 \）具有平滑的边界。特别是在半空间的情况下，对于速度矢量的切向分量，我们给出了弱解的正则性条件。