An Onsager type theorem for the Euler-Boussinesq equations in two spatial dimensions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916602919780352 |
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| author | Koley, Ujjwal |
| author_facet | Koley, Ujjwal |
| contents | In this article, we construct non-trivial weak solutions $(v, θ)$ to the inviscid Euler-Boussinesq system in two spatial dimensions. These solutions exhibit compact temporal support, thereby violating the conservation of the temperature's $L^p$-norm. Furthermore, the pair $(v, θ)$ resides in the Hölder space $C^γ(\mathbb R \times \mathbb T^2) \times C^γ(\mathbb R \times \mathbb T^2)$ for any exponent $γ<1/3$. The methodology integrates a Nash iteration scheme with a linear decoupling technique to achieve these results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2502_04803 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | An Onsager type theorem for the Euler-Boussinesq equations in two spatial dimensions Koley, Ujjwal Analysis of PDEs Mathematical Physics In this article, we construct non-trivial weak solutions $(v, θ)$ to the inviscid Euler-Boussinesq system in two spatial dimensions. These solutions exhibit compact temporal support, thereby violating the conservation of the temperature's $L^p$-norm. Furthermore, the pair $(v, θ)$ resides in the Hölder space $C^γ(\mathbb R \times \mathbb T^2) \times C^γ(\mathbb R \times \mathbb T^2)$ for any exponent $γ<1/3$. The methodology integrates a Nash iteration scheme with a linear decoupling technique to achieve these results. |
| title | An Onsager type theorem for the Euler-Boussinesq equations in two spatial dimensions |
| topic | Analysis of PDEs Mathematical Physics |
| url | https://arxiv.org/abs/2502.04803 |