Communications in Information and Systems

Volume 13 (2013)

Number 1

Special Issue in Honor of Marshall Slemrod: Part 1 of 4

Viscous and inviscid models in fluid-particle interaction

Pages: 45 – 78

DOI: https://dx.doi.org/10.4310/CIS.2013.v13.n1.a2

Authors

Joshua Ballew (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)

Konstantina Trivisa (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)

Abstract

Some recent developments in the study of fluid-particle interaction models are reviewed. A viscous model governed by the Navier- Stokes-Smoluchowski system and an inviscid model governed by the Euler-Smoluchowski system are presented and analyzed. For the viscous model, results on global existence, asymptotic behavior, singular limits and weak-strong uniqueness are discussed, whereas the analysis on the inviscid model deals with the issue of existence of smooth solutions.

2010 Mathematics Subject Classification

Primary 35Q84. Secondary 35D30.

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Published 28 May 2014