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This paper is concerned with the incompressible limit of the compressible Navier-Stokes-Smoluchowski equations with periodic boundary conditions in multidimensions. The authors establish the uniform stability of the local solution family which yields a lifespan of the Navier-Stokes-Smoluchowski system. Then, the local existence of strong solutions for the incompressible system with small initial data is rigorously proved via the incompressible limit. Furthermore, the authors obtain the convergence rates in the case without external force.

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In the paper, we establish a Serrin type criterion for strong solutions to a simplified density‐dependent Ericksen‐ Leslie system modeling incompressible, nematic liquid crystal materials in dimension two. Copyright © 2013 John Wiley & Sons, Ltd.