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Дифференциальные уравнения, динамические системы и оптимальное управление
Regularity criterion for weak solutions to the Navier-Stokes involving one velocity and one vorticity components
Ahmad M. Alghamdia, Sadek Galabc, Maria Alessandra Ragusac a Department of Mathematical Science, Faculty of Applied Science, Umm Alqura University, P. O. Box 14035, Makkah 21955, Saudi Arabia
b Department of Sciences Exactes, ENS of Mostaganem, University of Mostaganem, Box 227, Mostaganem 27000, Algeria
c Dipartimento di Matematica e Informatica, Università di Catania, Catania - Italy
Аннотация:
In this note, we are devoted to study the conditional regularity for the three dimensional Navier-Stokes in terms of the Morrey and $BMO$ spaces. More precisely, we show that if $u$ is a weak solution and $u_{3}\in L^{2}(0,T;BMO(\mathbb{R}^{3}))$ and $\omega _{3}\in L^{ \frac{2}{2-r}}(0,T;\mathcal{\dot{M}}_{2,\frac{3}{r}}(\mathbb{R}^{3}))$ with $0<r<1$, then $u$ is regular on $(0,T]$. This improves the available result by Zhang (2018) with $u_{3}\in L^{2}(0,T;L^{\infty }(\mathbb{R}^{3}))$ and $\omega _{3}\in L^{\frac{2}{2-r}}(0,T;L^{\frac{3}{r}}(\mathbb{R}^{3}))$ with $0<r<1$.
Ключевые слова:
Navier-Stokes equations, regularity criteria, Morrey space.
Поступила 18 марта 2022 г., опубликована 6 июня 2022 г.
Образец цитирования:
Ahmad M. Alghamdi, Sadek Gala, Maria Alessandra Ragusa, “Regularity criterion for weak solutions to the Navier-Stokes involving one velocity and one vorticity components”, Сиб. электрон. матем. изв., 19:1 (2022), 309–315
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr1501 https://www.mathnet.ru/rus/semr/v19/i1/p309
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