On the Cauchy Problem for the Pressureless Euler–Navier–Stokes System in the Whole Space

Young Pil Choi, Jinwook Jung

Research output: Contribution to journalArticlepeer-review


In this paper, we study the global Cauchy problem for a two-phase fluid model consisting of the pressureless Euler equations and the incompressible Navier–Stokes equations where the coupling of two equations is through the drag force. We establish the global-in-time existence and uniqueness of classical solutions for that system when the initial data are sufficiently small and regular. Main difficulties arise in the absence of pressure in the Euler equations. In order to resolve it, we properly combine the large-time behavior of classical solutions and the bootstrapping argument to construct the global-in-time unique classical solutions.

Original languageEnglish
Article number99
JournalJournal of Mathematical Fluid Mechanics
Issue number4
Publication statusPublished - 2021 Nov

Bibliographical note

Funding Information:
The work of Y.-P. Choi was supported by NRF Grant (No. 2017R1C1B2012918), POSCO Science Fellowship of POSCO TJ Park Foundation, and Yonsei University Research Fund of 2019-22-0212. The work of J. Jung was supported by NRF Grant (No. 2019R1A6A1A10073437).

Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics


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