A representation formula without pressure term is derived for regular solutions to the 3D time-dependent Oseen system in exterior Lipschitz domains. This formula is valid even if no boundary conditions are imposed. It is used in order to exhibit how the velocity decays pointwise in space. It turns out that the rate of this decay depends on \(L^p\)-integrability in time of the velocity. In addition, this work is the basis for successor papers dealing with spatial decay of \(L^q\)-weak solutions and mild solutions to the time-dependent Oseen system, and with \(L^2\)-strong solutions to the stability problem related to the Navier-Stokes system with Oseen term.

对于外部Lipschitz域中的3D时间相关Oseen系统的常规解，可以导出没有压力项的表示公式。即使没有施加边界条件，该公式也有效。它用于显示速度如何在空间中逐点衰减。事实证明，这种衰减的速率取决于速度时间的（L ^ p \）-可积性。此外，这项工作是后续论文处理\（L ^ q \）-时间依赖的Oseen系统的弱解和温和解以及\（L ^ 2 \）-强解的后继论文的基础。与带有Oseen项的Navier-Stokes系统有关的稳定性问题。