Strong well-posedness for a stochastic fluid-rigid body system via stochastic maximal regularity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909033847324672 |
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| author | Brandt, Felix Roy, Arnab |
| author_facet | Brandt, Felix Roy, Arnab |
| contents | We develop a rigorous analytical framework for a coupled stochastic fluid-rigid body system in $\mathbb{R}^3$. The model describes the motion of a rigid ball immersed in an incompressible Newtonian fluid subjected to both additive noise in the fluid and body equations and transport-type noise in the fluid equation. We establish local strong well-posedness of the resulting system by combining stochastic maximal $\mathrm{L}^p$-regularity theory with a decoupling approach for the associated fluid-structure operator. A key step is to prove the boundedness of the $\mathcal{H}^\infty$-calculus for this operator. In addition, we provide blow-up criteria for the maximal existence time of solutions. To our knowledge, this is the first rigorous treatment of strong solutions of stochastic fluid-structure interactions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2504_14676 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strong well-posedness for a stochastic fluid-rigid body system via stochastic maximal regularity Brandt, Felix Roy, Arnab Analysis of PDEs 35Q35, 74F10, 60H15, 35R60 We develop a rigorous analytical framework for a coupled stochastic fluid-rigid body system in $\mathbb{R}^3$. The model describes the motion of a rigid ball immersed in an incompressible Newtonian fluid subjected to both additive noise in the fluid and body equations and transport-type noise in the fluid equation. We establish local strong well-posedness of the resulting system by combining stochastic maximal $\mathrm{L}^p$-regularity theory with a decoupling approach for the associated fluid-structure operator. A key step is to prove the boundedness of the $\mathcal{H}^\infty$-calculus for this operator. In addition, we provide blow-up criteria for the maximal existence time of solutions. To our knowledge, this is the first rigorous treatment of strong solutions of stochastic fluid-structure interactions. |
| title | Strong well-posedness for a stochastic fluid-rigid body system via stochastic maximal regularity |
| topic | Analysis of PDEs 35Q35, 74F10, 60H15, 35R60 |
| url | https://arxiv.org/abs/2504.14676 |