论文标题
弯曲的薄域中的Navier-Stokes方程，第二部分：强大解决方案的全局存在
Navier-Stokes equations in a curved thin domain, Part II: global existence of a strong solution
论文作者
论文摘要
我们考虑在Navier的滑动边界条件下，在给定的闭合表面周围的三维弯曲薄域中的Navier-Stokes方程。当薄域的厚度足够小时，我们为大数据建立了强大解决方案的全球存在。我们还根据薄域的厚度明确显示了具有常数的强溶液的几个估计值。这些结果的证明是基于标准能量方法和对流和粘性术语的良好产品估计，此后是对平均操作员在薄方向的详细研究。我们使用平均操作员将薄域上的三维矢量场分解为几乎二维平均部分和残差部分，并得出了良好的估计值，这些估计值在产品估算的证明中起着重要作用。
We consider the Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under Navier's slip boundary conditions. When the thickness of the thin domain is sufficiently small, we establish the global existence of a strong solution for large data. We also show several estimates for the strong solution with constants explicitly depending on the thickness of the thin domain. The proofs of these results are based on a standard energy method and a good product estimate for the convection and viscous terms following from a detailed study of average operators in the thin direction. We use the average operators to decompose a three-dimensional vector field on the thin domain into the almost two-dimensional average part and the residual part, and derive good estimates for them which play an important role in the proof of the product estimate.
