On a Fluid-Particle Interaction Model: Global in Time Weak Solutions Within a Moving Domain in \(\mathbb{R}^{3}\)

  • Stefan Doboszczak
  • Konstantina TrivisaEmail author
Part of the Fields Institute Communications book series (FIC, volume 75)


A fluid-particle interaction model is presented for the evolution of particles dispersed in a fluid. The fluid flow is governed by the Navier-Stokes equations for a compressible fluid while the evolution of the particle densities is given by the Smoluchowski equation. The coupling between the dispersed and dense phases is obtained through the drag forces that the fluid and particles exert mutually. In the present context, the flow occupies a physical domain Ω t with boundary Γ t both of which vary in time. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior and viscosity in the weak formulation.


Weak Solution Weak Formulation Compressible Fluid Energy Inequality Moving Domain 
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The work of S.D. was supported in part by the National Science Foundation under the grant DMS-1211519 and by the John Osborn Memorial Summer Fellowship. K.T. gratefully acknowledges the support in part by the National Science Foundation under the grant DMS-1211519 and by the Simons Foundation under the Simons Fellows in Mathematics Award 267399.


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© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of MarylandCollege ParkUSA

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