Communications in Mathematical Physics

, Volume 340, Issue 2, pp 471–497 | Cite as

Analysis of an Incompressible Navier–Stokes–Maxwell–Stefan System

  • Xiuqing Chen
  • Ansgar JüngelEmail author


The Maxwell–Stefan equations for the molar fluxes, supplemented by the incompressible Navier–Stokes equations governing the fluid velocity dynamics, 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 different molar masses of the fluid components. 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.


Entropy Weak Solution Stokes Equation Molar Mass Global Existence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of SciencesBeijing University of Posts and TelecommunicationsBeijingChina
  2. 2.Institute for Analysis and Scientific ComputingVienna University of TechnologyViennaAustria

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