Global regularity for the one-dimensional stochastic Quantum-Navier-Stokes equations
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911760394485760 |
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| author | Donatelli, Donatella Pescatore, Lorenzo Spirito, Stefano |
| author_facet | Donatelli, Donatella Pescatore, Lorenzo Spirito, Stefano |
| contents | In this paper we prove the global in time well-posedness of strong solutions to the Quantum-Navier-Stokes equation driven by random initial data and stochastic external force. In particular, we first give a general local well-posedness result. Then, by means of the Bresch-Desjardins entropy, higher order energy estimates, and a continuation argument we prove that the density never vanishes, and thus that local strong solutions are indeed global. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10064 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global regularity for the one-dimensional stochastic Quantum-Navier-Stokes equations Donatelli, Donatella Pescatore, Lorenzo Spirito, Stefano Analysis of PDEs 35Q35, 60H15, 76M35 In this paper we prove the global in time well-posedness of strong solutions to the Quantum-Navier-Stokes equation driven by random initial data and stochastic external force. In particular, we first give a general local well-posedness result. Then, by means of the Bresch-Desjardins entropy, higher order energy estimates, and a continuation argument we prove that the density never vanishes, and thus that local strong solutions are indeed global. |
| title | Global regularity for the one-dimensional stochastic Quantum-Navier-Stokes equations |
| topic | Analysis of PDEs 35Q35, 60H15, 76M35 |
| url | https://arxiv.org/abs/2401.10064 |