发表机构
Clemson University（克莱姆森大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究周期条带上的热-波流固耦合系统，证明弱解全局存在性及直至H^3的Sobolev正则性，并指出因系统复杂性，高阶估计无法超越H^3。
AI 中文摘要
本文研究了一个定义在周期条带几何上的热-波流固耦合系统，并探讨尽管抛物型与双曲型正则性存在固有失配，是否仍能针对任意大的$s$值建立该耦合系统的高阶$H^s$估计。我们建立了弱解的全局存在性以及直至$H^3$水平的Sobolev正则性，据我们所知，这是目前为该系统建立的最高的正则性。我们进一步证明，即使对于任意正则的初始数据，无论是通过高阶生成元域$D(A^k)$（其中$k\in\mathbb{N}$）的半群方法，还是基于PDE的切向-法向恢复过程，由于耦合PDE系统的复杂性，都无法在$H^3$之外获得封闭的估计。
英文摘要
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 $k\in\mathbb{N}$ nor the PDE-based tangential-normal recovery procedure yields closed estimates beyond $H^3$ due to the complexities of the coupled PDE system.
