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

Young Pil Choi; Jinwook Jung

doi:10.1007/s00021-021-00624-9

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

Young Pil Choi, Jinwook Jung

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Article number	99
Journal	Journal of Mathematical Fluid Mechanics
Volume	23
Issue number	4
DOIs	https://doi.org/10.1007/s00021-021-00624-9
Publication status	Published - 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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10.1007/s00021-021-00624-9

Cite this

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abstract = "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.",

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

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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