Global well-posedness of 2D Navier-Stokes with Dirichlet boundary fractional noise
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866912430654750720 |
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| author | Agresti, Antonio Blessing, Alexandra Luongo, Eliseo |
| author_facet | Agresti, Antonio Blessing, Alexandra Luongo, Eliseo |
| contents | In this paper, we prove the global well-posedness and interior regularity for the 2D Navier-Stokes equations driven by a fractional noise acting as an inhomogeneous Dirichlet-type boundary condition. The model describes a vertical slice of the ocean with a relative motion between the two surfaces and can be thought of as a stochastic variant of the Couette flow. The relative motion of the surfaces is modeled by a Gaussian noise which is coloured in space and fractional in time with Hurst parameter greater than 3/4. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_03988 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of 2D Navier-Stokes with Dirichlet boundary fractional noise Agresti, Antonio Blessing, Alexandra Luongo, Eliseo Analysis of PDEs Probability In this paper, we prove the global well-posedness and interior regularity for the 2D Navier-Stokes equations driven by a fractional noise acting as an inhomogeneous Dirichlet-type boundary condition. The model describes a vertical slice of the ocean with a relative motion between the two surfaces and can be thought of as a stochastic variant of the Couette flow. The relative motion of the surfaces is modeled by a Gaussian noise which is coloured in space and fractional in time with Hurst parameter greater than 3/4. |
| title | Global well-posedness of 2D Navier-Stokes with Dirichlet boundary fractional noise |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2407.03988 |