Compressible stochastic fluid--structure interaction with transport noise and Navier slip: A stochastic-flow approach
Abstract
This paper establishes the existence of local martingale solutions for a three-dimensional stochastic fluid--structure interaction (FSI) problem coupling a viscous compressible isentropic fluid with an elastic shell through Navier-slip boundary conditions. The fluid and shell are perturbed by compatible Stratonovich transport noise. A stochastic-flow transformation removes the stochastic transport integrals and produces a pathwise random FSI system whose pullback coefficients are only Hölder continuous in time. We combine a multi-layer approximation scheme with localization on bounded-flow events and freezing of the random coefficients on short deterministic time subintervals. The shell transport fields are not required to generate isometries: the bending-energy martingale and Itô correction are controlled at the natural H2 level by commutator identities without derivative loss. Tightness is obtained in Jakubowski spaces, pressure compactness is proved through localized effective viscous flux, and the final artificial-pressure and penalty limit uses boundary-pressure tightness and H2-graph trace tools. For γ>3/2 and non-colliding initial data, we obtain a martingale solution up to an almost surely positive stopping time.
Related
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BibTeX
@misc{yong2026compressible,
title = {{Compressible stochastic fluid--structure interaction with transport noise and Navier slip: A stochastic-flow approach}},
author = {Chen Yong and Gao Hongjun},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.23485},
eprint = {2609.23485},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.23485},
}
RIS
TY - UNPB
TI - Compressible stochastic fluid--structure interaction with transport noise and Navier slip: A stochastic-flow approach
AU - Chen Yong
AU - Gao Hongjun
PY - 2026
DA - 2026/09/20
PB - arXiv
DO - 10.48550/arxiv.2609.23485
UR - https://arxiv.org/abs/2609.23485
AB - This paper establishes the existence of local martingale solutions for a three-dimensional stochastic fluid--structure interaction (FSI) problem coupling a viscous compressible isentropic fluid with an elastic shell through Navier-slip boundary conditions. The fluid and shell are perturbed by compatible Stratonovich transport noise. A stochastic-flow transformation removes the stochastic transport integrals and produces a pathwise random FSI system whose pullback coefficients are only Hölder continuous in time. We combine a multi-layer approximation scheme with localization on bounded-flow events and freezing of the random coefficients on short deterministic time subintervals. The shell transport fields are not required to generate isometries: the bending-energy martingale and Itô correction are controlled at the natural H^2 level by commutator identities without derivative loss. Tightness is obtained in Jakubowski spaces, pressure compactness is proved through localized effective viscous flux, and the final artificial-pressure and penalty limit uses boundary-pressure tightness and H^2-graph trace tools. For γ>3/2 and non-colliding initial data, we obtain a martingale solution up to an almost surely positive stopping time.
ER -