论文标题
从有限多种模式的观察结果确定Navier-Stokes方程的粘度
Determining the viscosity of the Navier-Stokes equations from observations of finitely many modes
论文作者
论文摘要
在这项工作中，我们询问并回答一个问题：液体的粘度是什么时候从其速度场的空间稀疏测量中确定的？我们使用确定映射（将数据映射到通过裸算法进行近似的映射到近似）来定义损失功能的确定映射（将数据映射到近似值）以数学上提出问题，以定义损失功能，该损失功能的最小化解决了鉴定真实粘度的倒数问题。我们给出了这个反问题良好性的先验条件。此外，我们表明损失功能的较小性暗示着靠近真实粘度。然后，我们提出了一种用于解决反问题并证明其收敛性的算法。
In this work, we ask and answer the question: when is the viscosity of a fluid uniquely determined from spatially sparse measurements of its velocity field? We pose the question mathematically as an optimization problem using the determining map (the mapping of data to an approximation made via a nudging algorithm) to define a loss functional, the minimization of which solves the inverse problem of identifying the true viscosity given the measurement data. We give explicit a priori conditions for the well-posedness of this inverse problem. In addition, we show that smallness of the loss functional implies proximity to the true viscosity. We then present an algorithm for solving the inverse problem and prove its convergence.
