Boundary Layer Criterion for the Low Mach Number and Inviscid Limits in Compressible Fluid-Rigid Body Interaction
Abstract
We investigate the simultaneous low Mach number and vanishing viscosity limit for a three-dimensional compressible viscous fluid interacting with a freely moving rigid body. The fluid satisfies the compressible Navier-Stokes equations and the no-slip condition on the body surface, while the body evolves according to Newton's laws driven by the fluid stresses. We establish convergence of finite-energy weak solutions to a strong solution of the corresponding incompressible Euler-rigid body system on its interval of existence. Assuming that the initial relative energy tends to zero, convergence holds under a Kato-type condition in a boundary layer whose thickness is proportional to the viscosity. This condition combines vanishing viscous dissipation with a weighted estimate on the fluid momentum relative to the rigid body motion. The proof uses the relative entropy method and a boundary layer corrector adapted to the fluid-rigid body coupling, providing a sufficient condition for convergence in relative energy as the Mach number and viscosity tend to zero simultaneously.
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BibTeX
@misc{bhandari2026boundary,
title = {{Boundary Layer Criterion for the Low Mach Number and Inviscid Limits in Compressible Fluid-Rigid Body Interaction}},
author = {Kuntal Bhandari and Šárka Nečasová and Arnab Roy},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35441},
eprint = {2610.35441},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35441},
}
RIS
TY - UNPB
TI - Boundary Layer Criterion for the Low Mach Number and Inviscid Limits in Compressible Fluid-Rigid Body Interaction
AU - Kuntal Bhandari
AU - Šárka Nečasová
AU - Arnab Roy
PY - 2026
DA - 2026/10/26
PB - arXiv
DO - 10.48550/arxiv.2610.35441
UR - https://arxiv.org/abs/2610.35441
AB - We investigate the simultaneous low Mach number and vanishing viscosity limit for a three-dimensional compressible viscous fluid interacting with a freely moving rigid body. The fluid satisfies the compressible Navier-Stokes equations and the no-slip condition on the body surface, while the body evolves according to Newton's laws driven by the fluid stresses. We establish convergence of finite-energy weak solutions to a strong solution of the corresponding incompressible Euler-rigid body system on its interval of existence. Assuming that the initial relative energy tends to zero, convergence holds under a Kato-type condition in a boundary layer whose thickness is proportional to the viscosity. This condition combines vanishing viscous dissipation with a weighted estimate on the fluid momentum relative to the rigid body motion. The proof uses the relative entropy method and a boundary layer corrector adapted to the fluid-rigid body coupling, providing a sufficient condition for convergence in relative energy as the Mach number and viscosity tend to zero simultaneously.
ER -