Dynamics of dissipative solutions to the Hardy-Sobolev parabolic equation
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912800829341696 |
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| author | Ikeda, Masahiro Niche, César J. Planas, Gabriela |
| author_facet | Ikeda, Masahiro Niche, César J. Planas, Gabriela |
| contents | We study the long-time behaviour of solutions to the Hardy-Sobolev parabolic equation in critical function spaces for any spatial dimension $d \geq 5$. By employing the Fourier splitting method, we establish precise decay rates for dissipative solutions, meaning those whose critical norm vanishes as time approaches infinity. Our findings offer a deeper understanding of the asymptotic properties and dissipation mechanisms governing this equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_02570 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of dissipative solutions to the Hardy-Sobolev parabolic equation Ikeda, Masahiro Niche, César J. Planas, Gabriela Analysis of PDEs We study the long-time behaviour of solutions to the Hardy-Sobolev parabolic equation in critical function spaces for any spatial dimension $d \geq 5$. By employing the Fourier splitting method, we establish precise decay rates for dissipative solutions, meaning those whose critical norm vanishes as time approaches infinity. Our findings offer a deeper understanding of the asymptotic properties and dissipation mechanisms governing this equation. |
| title | Dynamics of dissipative solutions to the Hardy-Sobolev parabolic equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.02570 |