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"Maxwell-Stefan meets Navier-Stokes" - Existence Results for Multicomponent Mixtures

I will present a model of motion of compressible multicomponent mixture based on the Navier-Stokes(-Fourier) equations coupled with the so-called Maxwell-Stefan system. The thermodynamics implies that the diffusion matrix appearing in the reaction-diffusion equations is non-symmetric, non positively defined, and cross-diffusion effects must be strongly marked. Mathematical analysis of the system encounters a problem of hyperbolic deviation in the species mass conservation equations. Moreover, we consider density-dependent viscosity coefficients vanishing on vacuum. We prove sequential stability of weak solutions and a global-in-time existence of weak solutions for a singular internal pressure.

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