X. Chen, A. Jüngel:

"Analysis of an incompressible Navier-Stokes-Maxwell-Stefan system";

in: "ASC Report 41/2013", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2013, ISBN: 978-3-902627-06-3, 1 - 27.

The incompressible Navier-Stokes equations coupled to the Maxwell-Stefan relations for the molar fluxes are analyzed in bounded domains with no-flux boundary conditions. The system models the dynamics of a multicomponent gaseous mixture under isothermal conditions. The global-in-time existence of bounded weak solutions to the

strongly coupled model and their exponential decay to the homogeneous steady state are proved. The mathematical difficulties are due to the singular Maxwell-Stefan diffusion matrix, the cross-diffusion terms, and the Navier-Stokes coupling. The key idea of the proof is the use of a new entropy functional and entropy variables, which allows for a proof of positive lower and upper bounds of the mass densities without the use of a maximum principle.

Incompressible Navier-Stokes equations, Maxwell-Stefan equations, crossdiffusion, entropy dissipation, entropy variables, global existence of solutions, long-time behavior of solutions.

http://www.asc.tuwien.ac.at/preprint/2013/asc41x2013.pdf

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