Zeng, Zirong Local mild solutions to three-dimensional magnetohydrodynamic system in Morrey spaces. (English) Zbl 1473.35464 Math. Methods Appl. Sci. 44, No. 7, 5326-5339 (2021). Summary: In this article, we study the Cauchy problem of three-dimensional (3-D) incompressible magnetohydrodynamic system with infinite energy initial data. Via some elaborate analysis of the time evolution of both the vorticity \(\omega : = \nabla \times u\) and the current density \(j = : \nabla \times b\), the local-in-time well-posedness of mild solutions with arbitrarily large initial data in Morrey spaces is established. MSC: 35Q35 PDEs in connection with fluid mechanics 35B40 Asymptotic behavior of solutions to PDEs 35L60 First-order nonlinear hyperbolic equations Keywords:incompressible magnetohydrodynamic equations; Morrey spaces; mild solutions PDFBibTeX XMLCite \textit{Z. Zeng}, Math. Methods Appl. Sci. 44, No. 7, 5326--5339 (2021; Zbl 1473.35464) Full Text: DOI