In this paper, we consider the Navier–Stokes equation with memory term in a three-dimensional bounded domain. The equation is the so-called Oldroyd fluid model equation, which can describe the stress relaxation as well as the retardation of deformation due to the memory term. For this equation we considered the inverse problem for recovering the kernel of memory term in this model equation from the measurement described as the integral over determination condition. We obtained a local in time existence and uniqueness for this inverse problem.

中文翻译：

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具有记忆项的Navier–Stokes方程反问题的局部可解性

在本文中，我们考虑在三维有界域中具有记忆项的Navier-Stokes方程。该方程是所谓的Oldroyd流体模型方程，可以描述应力松弛以及由于记忆项引起的变形延迟。对于该方程式，我们考虑了从描述为积分超过确定条件的测量中恢复该模型方程式中记忆项内核的反问题。我们获得了该逆问题在时间上的局部存在性和唯一性。