Quantitative bounds for critically bounded solutions to the three-dimensional Navier-Stokes equations in Lorentz spaces
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866909056231276544 |
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| author | Feng, Wen He, Jiao Wang, Weinan |
| author_facet | Feng, Wen He, Jiao Wang, Weinan |
| contents | In this paper, we prove a quantitative regularity theorem and a blow-up criterion of classical solutions for the three-dimensional Navier-Stokes equations. By adapting the strategy developed by Tao in [20], we obtain an explicit blow-up rate in the setting of critical Lorentz spaces $L^{3, q_{0}}(\mathbb R^3)$ with $3 \leq q_0 < \infty $. Our results improve the previous regularity in critical Lebesgue spaces $L^3(\mathbb R^3)$ in [20] and quantify the qualitative result by Phuc in [16]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2201_04656 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Quantitative bounds for critically bounded solutions to the three-dimensional Navier-Stokes equations in Lorentz spaces Feng, Wen He, Jiao Wang, Weinan Analysis of PDEs In this paper, we prove a quantitative regularity theorem and a blow-up criterion of classical solutions for the three-dimensional Navier-Stokes equations. By adapting the strategy developed by Tao in [20], we obtain an explicit blow-up rate in the setting of critical Lorentz spaces $L^{3, q_{0}}(\mathbb R^3)$ with $3 \leq q_0 < \infty $. Our results improve the previous regularity in critical Lebesgue spaces $L^3(\mathbb R^3)$ in [20] and quantify the qualitative result by Phuc in [16]. |
| title | Quantitative bounds for critically bounded solutions to the three-dimensional Navier-Stokes equations in Lorentz spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2201.04656 |