论文标题
半空间中非平稳stokes系统的绿色张量
The Green tensor of the nonstationary Stokes system in the half space
论文作者
论文摘要
我们证明了（不受限制的）绿色张量和半空间中非平稳stokes系统的相关压力张量的第一个重点估计值，因为每个空间维度都大于一个。不一定假定力场是电磁阀。关键是找到合适的绿色张量公式，该公式最大化切向衰减，特别是绿色张量衍生物的整合性。凭借其刻度的估计，我们显示了绿色张量的对称性，进而改善了刻度的估计。我们还研究了解决方案如何融合到初始数据，以及作用于螺线管载体场的（无限的）限制的绿色张量。作为应用程序，我们提供了新的证明，以$ l^q $，尖锐的衰减以及半空间中均匀的本地$ l^q $空间的Navier-Stokes方程式存在。
We prove the first ever pointwise estimates of the (unrestricted) Green tensor and the associated pressure tensor of the nonstationary Stokes system in the half-space, for every space dimension greater than one. The force field is not necessarily assumed to be solenoidal. The key is to find a suitable Green tensor formula which maximizes the tangential decay, showing in particular the integrability of Green tensor derivatives. With its pointwise estimates, we show the symmetry of the Green tensor, which in turn improves pointwise estimates. We also study how the solutions converge to the initial data, and the (infinitely many) restricted Green tensors acting on solenoidal vector fields. As applications, we give new proofs of existence of mild solutions of the Navier-Stokes equations in $L^q$, pointwise decay, and uniformly local $L^q$ spaces in the half-space.
