The Cauchy problem for the pressureless Euler/isentropic Navier-Stokes equations

Young Pil Choi, Bongsuk Kwon

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We present a new hydrodynamic model consisting of the pressureless Euler equations and the isentropic compressible Navier-Stokes equations where the coupling of two systems is through the drag force. This coupled system can be derived, in the hydrodynamic limit, from the particle-fluid equations that are frequently used to study the medical sprays, aerosols and sedimentation problems. For the proposed system, we first construct the local-in-time classical solutions in an appropriate L2 Sobolev space. We also establish the a priori large-time behavior estimate by constructing a Lyapunov functional measuring the fluctuation of momentum and mass from the averaged quantities, and using this together with the bootstrapping argument, we obtain the global classical solution. The large-time behavior estimate asserts that the velocity functions of the pressureless Euler and the compressible Navier-Stokes equations are aligned exponentially fast as time tends to infinity.

Original languageEnglish
Pages (from-to)654-711
Number of pages58
JournalJournal of Differential Equations
Volume261
Issue number1
DOIs
Publication statusPublished - 2016 Jul 5

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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