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

在本文中，我们将对多组分等温流体中传质的研究扩展到不可压缩的情况。对于混合物，不可压缩性定义为平均体积与压力的独立性，部分质量密度的加权总和保持恒定。在这种类型的模型中，Navier–Stokes方程中的速度场不是螺线管的，并且由于物质的比体积不同，压力仍通过代数公式与密度保持联系。通过改变运输问题中的变量，我们等效地重新制定了PDE系统，以消除影响密度的正性和不可压缩性约束，并证明了两种类型的结果：强解类中的实时局部适时性，