On the global solvability of the generalised Navier-Stokes system in critical Besov spaces
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| Format: | Preprint |
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2025
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| _version_ | 1866910808266506240 |
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| author | Zhang, Huiyang Cao, SHiwei Zhang, Qinghua |
| author_facet | Zhang, Huiyang Cao, SHiwei Zhang, Qinghua |
| contents | This paper is devoted to the global solvability of the Navier-Stokes system with fractional Laplacian $(-Δ)^α$ in $\mathbb{R}^{n}$ for $n\geq2$, where the convective term has the form $(|u|^{m-1}u)\cdot\nabla u$ for $m\geq1$. By establishing the estimates for the difference $|u_{1}|^{m-1}u_{1}-|u_{2}|^{m-1}u_{2}$ in homogeneous Besov spaces, and employing the maximal regularity property of $(-Δ)^α$ in Lorentz spaces, we prove global existence and uniqueness of the strong solution of the Navier-Stokes in critical Besov spaces for both $m=1$ and $m>1$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_00324 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the global solvability of the generalised Navier-Stokes system in critical Besov spaces Zhang, Huiyang Cao, SHiwei Zhang, Qinghua Analysis of PDEs Functional Analysis This paper is devoted to the global solvability of the Navier-Stokes system with fractional Laplacian $(-Δ)^α$ in $\mathbb{R}^{n}$ for $n\geq2$, where the convective term has the form $(|u|^{m-1}u)\cdot\nabla u$ for $m\geq1$. By establishing the estimates for the difference $|u_{1}|^{m-1}u_{1}-|u_{2}|^{m-1}u_{2}$ in homogeneous Besov spaces, and employing the maximal regularity property of $(-Δ)^α$ in Lorentz spaces, we prove global existence and uniqueness of the strong solution of the Navier-Stokes in critical Besov spaces for both $m=1$ and $m>1$ |
| title | On the global solvability of the generalised Navier-Stokes system in critical Besov spaces |
| topic | Analysis of PDEs Functional Analysis |
| url | https://arxiv.org/abs/2502.00324 |