Abstract
Based on the construction of Bourgain and Pavlović [1] we show that the solutions to the Cauchy problem for the three-dimensional incompressible magneto-hydrodynamics (MHD) system can develop different types of norm inflations in $\dot{B}_{\infty}^{-1, \infty}$. In particular the magnetic field can develop norm inflation in a short time even when the velocity remains small and vice versa. Efforts are made to present a very expository development of the ingenious construction of Bourgain and Pavlović in [1].
Citation
Mimi Dai. Jie Qing. Maria E. Schonbek. "Norm inflation for incompressible magneto-hydrodynamic system in $\dot{B}_{\infty}^{-1,\infty}$." Adv. Differential Equations 16 (7/8) 725 - 746, July/August 2011. https://doi.org/10.57262/ade/1355703204
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