Noise-Driven Free Boundaries In The Compressible Navier-Stokes Equations
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914545134469120 |
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| author | Del Sarto, Gianmarco Hieber, Matthias Zöchling, Tarek |
| author_facet | Del Sarto, Gianmarco Hieber, Matthias Zöchling, Tarek |
| contents | A stochastic free-boundary problem for the three-dimensional barotropic compressible Navier--Stokes equations is studied. The main feature of the model is that the free boundary is transported by a Stratonovich stochastic flow, so that the noise enters the kinematic boundary condition and hence the evolution of the moving domain. An additional Itô forcing in the momentum equation is also allowed. The problem is transformed by a stochastic Lagrangian map generated by the velocity and the transport vector fields. In these coordinates the density is represented through the Jacobian of the flow, and the remaining system is solved by combining stochastic maximal regularity, deterministic %\rL^p%-%\rL^q$ estimates, and a localized contraction argument. Local pathwise well-posedness is obtained up to an a.s. positive stopping time, with strictly positive density and pathwise uniqueness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07953 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Noise-Driven Free Boundaries In The Compressible Navier-Stokes Equations Del Sarto, Gianmarco Hieber, Matthias Zöchling, Tarek Analysis of PDEs 35Q30, 35R60, 35R35, 60H15, 76N10 A stochastic free-boundary problem for the three-dimensional barotropic compressible Navier--Stokes equations is studied. The main feature of the model is that the free boundary is transported by a Stratonovich stochastic flow, so that the noise enters the kinematic boundary condition and hence the evolution of the moving domain. An additional Itô forcing in the momentum equation is also allowed. The problem is transformed by a stochastic Lagrangian map generated by the velocity and the transport vector fields. In these coordinates the density is represented through the Jacobian of the flow, and the remaining system is solved by combining stochastic maximal regularity, deterministic %\rL^p%-%\rL^q$ estimates, and a localized contraction argument. Local pathwise well-posedness is obtained up to an a.s. positive stopping time, with strictly positive density and pathwise uniqueness. |
| title | Noise-Driven Free Boundaries In The Compressible Navier-Stokes Equations |
| topic | Analysis of PDEs 35Q30, 35R60, 35R35, 60H15, 76N10 |
| url | https://arxiv.org/abs/2605.07953 |