×

Local mild solutions to three-dimensional magnetohydrodynamic system in Morrey spaces. (English) Zbl 1473.35464

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
PDFBibTeX XMLCite
Full Text: DOI