Well-posedness analysis of multicomponent incompressible flow models

Abstract In this paper, we extend our study of mass transport in multicomponent isothermal fluids to the incompressible case. For a mixture, incompressibility is defined as independence average volume on pressure, and weighted sum partial densities stays constant. type models, velocity field Navier–Stokes equations not solenoidal and, due different specific volumes species, pressure remains connected by algebraic formula. By means change variables problem, equivalently reformulate PDE system eliminate positivity constraints affecting density, prove two results: local-in-time well-posedness classes strong solutions, global-in-time existence solutions for initial data sufficiently close smooth equilibrium solution.