A regularity criterion of the 3D MHD equations involving one velocity and one current density component in Lorentz space
| Autor: | Agarwal, R., Gala, S., Ragusa, M. A. |
|---|---|
| Rok vydání: | 2020 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00033-020-01318-4 |
| Popis: | In this paper, we study the regularity criterion of weak solutions to the three-dimensional (3D) MHD equations. It is proved that the solution $(u,b)$ becomes regular provided that one velocity and one current density component of the solution satisfy% \begin{equation} u_{3}\in L^{\frac{30\alpha }{7\alpha -45}}\left( 0,T;L^{\alpha ,\infty }\left( \mathbb{R}^{3}\right) \right) \text{ \ \ \ with \ \ }\frac{45}{7}% \leq \alpha \leq \infty , \label{eq01} \end{equation}% and \begin{equation} j_{3}\in L^{\frac{2\beta }{2\beta -3}}\left( 0,T;L^{\beta ,\infty }\left( \mathbb{R}^{3}\right) \right) \text{ \ \ \ with \ \ }\frac{3}{2}\leq \beta \leq \infty , \label{eq02} \end{equation}% which generalize some known results. Comment: Zeitschrift f\"ur angewandte Mathematik und Physik |
| Databáze: | arXiv |
| Externí odkaz: |
|