Correctness of the Mathematical Model of a Weakly Compressible Viscoelastic Maxwell Medium
Abstract
A mathematical model of barotropic medium motion with medium density close to a constant is developed on the basis of the model of compressible viscoelastic Maxwell medium with constant dynamic viscosity and relaxation time. Medium behavior is described by the velocity vector, the pressure, and the stress tensor. The relaxation relation for a compressible medium is produced for the entire stress tensor without the selection of a deviator in it. A linearization of the system of equations describing the two-dimensional motion of a compressible viscoelastic Maxwell medium was carried out to describe a weakly compressible medium. The linearization is carried out for the state of rest with a constant nonzero density. It results in the equation for determining the pressure and a symmetric hyperbolic linear system for components of the velocity vector and the stress tensor. Hyperbolicity and symmetric form of the obtained system are preserved, thus, allow using the well-developed theory of hyperbolic equations. Using the linear approximation framework, the uniqueness domain of the Cauchy problem is found, and the correctness condition of the initial boundary value problem for the mathematical model of the two-dimensional motion of a weakly compressible viscoelastic Maxwell medium is obtained.
DOI 10.14258/izvasu(2018)1-15
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