Unique solvability of the initial-boundary value problem for one-dimensional barotropic equations of dynamics of compressible viscous multicomponent media
0000-0003-3833-0390 In the present paper, we consider the initial-boundary value problem for a one-dimensional model of barotropic dynamics of compressible viscous multicomponent media, described by a system of equations that generalizes the Navier-Stokes equations. Unlike the Navier-Stokes equations, where viscosity is a scalar quantity, in the multicomponent case the viscosities form a viscosity matrix reflecting the composite structure of the viscous stress tensors. This leads to the presence of higher-order derivatives of the velocities of all \linebreak components in the equations under study, which substantially complicates the mathematical analysis. The diagonal entries of the viscosity matrix account for the viscous friction inside each component, while the off-diagonal entries account for the intercomponent viscous interaction.In the case of a diagonal viscosity matrix, the components are coupled only through lower-order terms, which simplifies the situation significantly. The present study is devoted to establishing the existence and uniqueness of a solution to the initial-boundary value problem for one-dimensional barotropic equations of dynamics of compressible viscous multicomponent media in the more general case where the viscosity matrix has a non-diagonal structure.
УДК 517.9
Keywords: initial-boundary value problem, existence and uniqueness theorem, barotropic compressible viscous multicomponent medium