Prodi--Serrin condition for 3D Navier--Stokes equations via one directional derivative of velocity
| Autor: | Hui, Chen, Wenjun, Le, Chenyin, Qian |
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| Rok vydání: | 2021 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | In this paper, we consider the conditional regularity of weak solution to the 3D Navier--Stokes equations. More precisely, we prove that if one directional derivative of velocity, say $\partial_3 u,$ satisfies $\partial_3 u \in L^{p_0,1}(0,T; L^{q_0}(\mathbb{R}^3))$ with $\frac{2}{p_{0}}+\frac{3}{q_{0}}=2$ and $\frac{3}{2} |
| Databáze: | arXiv |
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