Existence of Weak Solutions and Higher-Order Regularity for a Heat-Wave Fluid-Structure Interaction System on a Periodic Strip
Abstract
In this paper, we study a heat-wave fluid-structure interaction system posed on a periodic strip geometry and investigate whether higher-order Hs-estimates for arbitrarily large values of s can be established for the coupled system despite the inherent mismatch of parabolic and hyperbolic regularity. We establish global existence of weak solutions and Sobolev regularity up to the H3-level, which, to the best of our knowledge, is the highest regularity currently established for this system. We further show that, even for arbitrarily regular initial data, neither the semigroup approach through higher-order generator domains D(Ak) with k∈ℕ nor the PDE-based tangential-normal recovery procedure yields closed estimates beyond H3 due to the complexities of the coupled PDE system.
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BibTeX
@misc{rahman2026existence,
title = {{Existence of Weak Solutions and Higher-Order Regularity for a Heat-Wave Fluid-Structure Interaction System on a Periodic Strip}},
author = {Mohammad Mahabubur Rahman},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20627},
eprint = {2609.20627},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20627},
}
RIS
TY - UNPB
TI - Existence of Weak Solutions and Higher-Order Regularity for a Heat-Wave Fluid-Structure Interaction System on a Periodic Strip
AU - Mohammad Mahabubur Rahman
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20627
UR - https://arxiv.org/abs/2609.20627
AB - In this paper, we study a heat-wave fluid-structure interaction system posed on a periodic strip geometry and investigate whether higher-order H^s-estimates for arbitrarily large values of s can be established for the coupled system despite the inherent mismatch of parabolic and hyperbolic regularity. We establish global existence of weak solutions and Sobolev regularity up to the H^3-level, which, to the best of our knowledge, is the highest regularity currently established for this system. We further show that, even for arbitrarily regular initial data, neither the semigroup approach through higher-order generator domains D(A^k) with k∈ℕ nor the PDE-based tangential-normal recovery procedure yields closed estimates beyond H^3 due to the complexities of the coupled PDE system.
ER -