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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2508.07025 |
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| _version_ | 1866912530527420416 |
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| author | Tartaglione, Alfonsina |
| author_facet | Tartaglione, Alfonsina |
| contents | By means of an $L^1-L^\infty$ duality argument, it is proved that, in a suitable planar domain $Ω$, the solution $u$ to the IBVP associated to the Navier-Stokes equations, with initial datum $u_0\in L^2(Ω)$, satisfies the following estimate $$ \left(\int_0^{+\infty}\|u(τ)\|_\infty^2{\hbox {d}}τ\right)^{1/2}\le c(1+\|u_0\|_2)\|u_0\|_2, $$ proved by R. Farwig and Y. Giga [Algebra i Analiz, 36, 289-307 (2024)] for bounded domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07025 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the 2D initial boundary value problem for the Navier-Stokes equations: square in time integrability of the maximum norm of the solutions with finite energy Tartaglione, Alfonsina Analysis of PDEs By means of an $L^1-L^\infty$ duality argument, it is proved that, in a suitable planar domain $Ω$, the solution $u$ to the IBVP associated to the Navier-Stokes equations, with initial datum $u_0\in L^2(Ω)$, satisfies the following estimate $$ \left(\int_0^{+\infty}\|u(τ)\|_\infty^2{\hbox {d}}τ\right)^{1/2}\le c(1+\|u_0\|_2)\|u_0\|_2, $$ proved by R. Farwig and Y. Giga [Algebra i Analiz, 36, 289-307 (2024)] for bounded domains. |
| title | On the 2D initial boundary value problem for the Navier-Stokes equations: square in time integrability of the maximum norm of the solutions with finite energy |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2508.07025 |