Compressible Euler equations interacting with incompressible flow

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11 Citations (Scopus)


We investigate the global existence and large-time behavior of clas- sical solutions to the compressible Euler equations coupled to the incompress- ible Navier-Stokes equations. The coupled hydrodynamic equations are rigor- ously derived in [1] as the hydrodynamic limit of the Vlasov/incompressible Navier-Stokes system with strong noise and local alignment. We prove the existence and uniqueness of global classical solutions of the coupled system under suitable assumptions. As a direct consequence of our result, we can con- clude that the estimates of hydrodynamic limit studied in [1] hold for all time. For the large-time behavior of the classical solutions, we show that two fluid velocities will be aligned with each other exponentially fast as time evolves.

Original languageEnglish
Pages (from-to)335-358
Number of pages24
JournalKinetic and Related Models
Issue number2
Publication statusPublished - 2015

Bibliographical note

Publisher Copyright:
© American Institute of Mathematical Sciences.

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modelling and Simulation


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