Fractional regularity, global persistence, and asymptotic properties of the Boussinesq equations on bounded domains
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866917918110908416 |
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| author | Aydın, Mustafa Sencer Jayanti, Pranava Chaitanya |
| author_facet | Aydın, Mustafa Sencer Jayanti, Pranava Chaitanya |
| contents | We address the long-time behavior of the 2D Boussinesq system, which consists of the incompressible Navier-Stokes equations driven by a non-diffusive density. We construct globally persistent solutions on a smooth bounded domain, when the initial data belongs to $(H^k\cap V)\times H^k$ for $k\in\mathbb{N}$ and $H^s\times H^s$ for $0<s<2$. The proofs use parabolic maximal regularity and specific compatibility conditions at the initial time. Additionally, we also deduce various asymptotic properties of the velocity and density in the long-time limit and present a necessary and sufficient condition for the convergence to a steady state. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_12509 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Fractional regularity, global persistence, and asymptotic properties of the Boussinesq equations on bounded domains Aydın, Mustafa Sencer Jayanti, Pranava Chaitanya Analysis of PDEs We address the long-time behavior of the 2D Boussinesq system, which consists of the incompressible Navier-Stokes equations driven by a non-diffusive density. We construct globally persistent solutions on a smooth bounded domain, when the initial data belongs to $(H^k\cap V)\times H^k$ for $k\in\mathbb{N}$ and $H^s\times H^s$ for $0<s<2$. The proofs use parabolic maximal regularity and specific compatibility conditions at the initial time. Additionally, we also deduce various asymptotic properties of the velocity and density in the long-time limit and present a necessary and sufficient condition for the convergence to a steady state. |
| title | Fractional regularity, global persistence, and asymptotic properties of the Boussinesq equations on bounded domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.12509 |