Suitable weak solutions and low stratification singular limit for a fluid particle interaction model

Ballew, Joshua; Trivisa, Konstantina

doi:10.1090/S0033-569X-2012-01310-2

Authors: Joshua Ballew and Konstantina Trivisa
Journal: Quart. Appl. Math. 70 (2012), 469-494
MSC (2010): Primary 54C40, 14E20; Secondary 46E25, 20C20
DOI: https://doi.org/10.1090/S0033-569X-2012-01310-2
Published electronically: May 10, 2012
MathSciNet review: 2986131
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Abstract: This article deals with a fluid-particle interaction model for the evolution of particles dispersed in a viscous compressible fluid within the physical space $\Omega \subset \mathbb {R}^3.$ The system is expressed by the continuity equation, the balance of momentum and the so-called Smoluchowski equation for the evolution of particles. The coupling between the dispersed and dense phases is obtained through the drag forces that the fluid and the particles exert mutually by the action-reaction principle. Using the relative entropy method of Dafermos and DiPerna, the global-in-time existence of suitable weak solutions is presented under reasonable physical assumptions on the initial data, the physical domain, and the external potential. In addition, the low Mach number and low stratification limits of the system are established rigorously for both bounded and unbounded domains.

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