Maxwell's Fluid Mechanics

The analogy between the standard hydromechanical equations and the system of Maxwell's equations has long been noticed and discussed in a number of publications. In this regard in [7] an alternative model of a viscous fluid was presented, based on the description of a moving medium using a system of Maxwell-type equations. The appearance of such models expands the researcher's arsenal, especially since, unlike the standard hydromechanical model, which is a nonlinear system of partial differential equations of the second order, the alternative model is a linear system of equations of the first order. In this paper, this model is studied from different viewpoints. First of all, various problem posing and algorithms for their integration are considered. An example of using this model to describe known shear flows is discussed separately. The results obtained are compared with the classical ones (Couette and Poiseuille flows). The linearity of the proposed model makes it easy to use the Fourier transform to solve it. Such an approach is demonstrated in the last section of this paper. PACS numbers: 40., 47., 47.10.-g, 47.10.A-