We study the potential flow of an ideal fluid through a domain that consists of a reservoir and a pipe connected to it. The ratio of the pipe’s thickness and its length is considered as a small parameter. Using the rigorous asymptotic analysis with respect to that small parameter, we derive an effective model governing the the junction between a 1D and a 3D fluid domain. The obtained boundary-value problem has a measure boundary condition with Dirac mass concentrated in the junction point and is understood in the very-weak sense.

中文翻译：

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通过非常弱的公式对3D–1D结进行建模

我们研究了理想流体流过由油层和与其相连的管道组成的区域的潜在流量。管道的厚度与长度之比被认为是一个很小的参数。使用针对该小参数的严格渐近分析，我们得出了一个有效的模型，该模型控制1D和3D流体域之间的交界处。所获得的边界值问题具有狄拉克质量集中在结点处的度量边界条件，并且在非常弱的意义上被理解。