Non-Algebraic Decay for Solutions to the Navier-Stokes Equations
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918504951709696 |
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| author | Brandolese, Lorenzo Pageard, Matthieu Perusato, Cilon F. |
| author_facet | Brandolese, Lorenzo Pageard, Matthieu Perusato, Cilon F. |
| contents | Around forty years ago, Michael Wiegner provided, in a seminal paper, sharp algebraic decay rates for solutions of the Navier--Stokes equations, showing that these solutions behave asymptotically like the solutions of the heat equation with the same data as $t\to+\infty$, in the $L^2$-norm, up to some critical decay rate. In the present paper, we close a gap that appears in the conclusion of Wiegner's theorem in the 2D case, for solutions with non-algebraic decay rate. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2512_21312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-Algebraic Decay for Solutions to the Navier-Stokes Equations Brandolese, Lorenzo Pageard, Matthieu Perusato, Cilon F. Analysis of PDEs 35B40 (primary), 35Q35 (secondary) Around forty years ago, Michael Wiegner provided, in a seminal paper, sharp algebraic decay rates for solutions of the Navier--Stokes equations, showing that these solutions behave asymptotically like the solutions of the heat equation with the same data as $t\to+\infty$, in the $L^2$-norm, up to some critical decay rate. In the present paper, we close a gap that appears in the conclusion of Wiegner's theorem in the 2D case, for solutions with non-algebraic decay rate. |
| title | Non-Algebraic Decay for Solutions to the Navier-Stokes Equations |
| topic | Analysis of PDEs 35B40 (primary), 35Q35 (secondary) |
| url | https://arxiv.org/abs/2512.21312 |