Low Mach number limit of a two-phase flow model in ℝ3
Abstract
We study the simultaneous low Mach number limit of a compressible Navier--Stokes--Euler two-phase system in ℝ3, in which the pressure terms in both phases are scaled by ε−2. For sufficiently small H3-perturbations around the constant equilibrium, we establish the global well-posedness of the scaled compressible system and derive global energy-dissipation estimates that are uniform with respect to the Mach number ε. A key feature of the analysis is the degenerate dissipation structure: viscosity acts only on the Navier--Stokes phase, while the drag coupling transfers dissipation to the inviscid Euler phase through the relaxation mode. We then prove the global well-posedness and large-time decay of the limiting incompressible two-phase system, and show that the relative velocity u−ω decays faster than the full velocity pair. Finally, for the well-prepared initial data, we introduce pressure-corrected acoustic variables to remove the singular pressure mismatch and establish a global-in-time H2-error. As a result, the scaled compressible solutions converge uniformly in time to the corresponding solution of the limiting incompressible system.
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BibTeX
@misc{li2026mach,
title = {{Low Mach number limit of a two-phase flow model in $\mathbbR^3$}},
author = {Fucai Li and Jinkai Ni and Zhipeng Zhang and Zhu Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.39900},
eprint = {2609.39900},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.39900},
}
RIS
TY - UNPB
TI - Low Mach number limit of a two-phase flow model in ℝ^3
AU - Fucai Li
AU - Jinkai Ni
AU - Zhipeng Zhang
AU - Zhu Zhang
PY - 2026
DA - 2026/09/30
PB - arXiv
DO - 10.48550/arxiv.2609.39900
UR - https://arxiv.org/abs/2609.39900
AB - We study the simultaneous low Mach number limit of a compressible Navier--Stokes--Euler two-phase system in ℝ^3, in which the pressure terms in both phases are scaled by ε^−2. For sufficiently small H^3-perturbations around the constant equilibrium, we establish the global well-posedness of the scaled compressible system and derive global energy-dissipation estimates that are uniform with respect to the Mach number ε. A key feature of the analysis is the degenerate dissipation structure: viscosity acts only on the Navier--Stokes phase, while the drag coupling transfers dissipation to the inviscid Euler phase through the relaxation mode. We then prove the global well-posedness and large-time decay of the limiting incompressible two-phase system, and show that the relative velocity u−ω decays faster than the full velocity pair. Finally, for the well-prepared initial data, we introduce pressure-corrected acoustic variables to remove the singular pressure mismatch and establish a global-in-time H^2-error. As a result, the scaled compressible solutions converge uniformly in time to the corresponding solution of the limiting incompressible system.
ER -