Global well-posedness for the Navier-Stokes system in new critical mixed-norm Besov spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912284202237952 |
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| author | Aurazo-Alvarez, Leithold L. Neves, Wladimir |
| author_facet | Aurazo-Alvarez, Leithold L. Neves, Wladimir |
| contents | In this work, we proved the existence of a unique global mild solution of the d-dimensional incompressible Navier-Stokes equations, for small initial data in Besov type spaces based on mixed-Lebesgue spaces; namely, mixed-norm Besov-Lebesgue spaces and also mixed-norm Fourier-Besov-Lebesgue spaces. The main tools are the Bernstein's type inequalities, Bony's paraproduct to estimate the bilinear term and a fixed point scheme in order to get the well-posedness. Our results complement and cover previous and recents result on (Fourier-)Besov spaces and, for instance, provide a new class of initial data possibly not included in BMO^{-1}(R^3) but continuously included in \dot{B}^{-1}_{\infty,infty}(R^3). |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_16362 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global well-posedness for the Navier-Stokes system in new critical mixed-norm Besov spaces Aurazo-Alvarez, Leithold L. Neves, Wladimir Analysis of PDEs In this work, we proved the existence of a unique global mild solution of the d-dimensional incompressible Navier-Stokes equations, for small initial data in Besov type spaces based on mixed-Lebesgue spaces; namely, mixed-norm Besov-Lebesgue spaces and also mixed-norm Fourier-Besov-Lebesgue spaces. The main tools are the Bernstein's type inequalities, Bony's paraproduct to estimate the bilinear term and a fixed point scheme in order to get the well-posedness. Our results complement and cover previous and recents result on (Fourier-)Besov spaces and, for instance, provide a new class of initial data possibly not included in BMO^{-1}(R^3) but continuously included in \dot{B}^{-1}_{\infty,infty}(R^3). |
| title | Global well-posedness for the Navier-Stokes system in new critical mixed-norm Besov spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.16362 |