### Norm inflation for incompressible magneto-hydrodynamic system in $\dot{B}_{\infty}^{-1,\infty}$

#### 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].

#### Article information

Source
Adv. Differential Equations, Volume 16, Number 7/8 (2011), 725-746.

Dates
First available in Project Euclid: 17 December 2012

Dai, Mimi; Qing, Jie; Schonbek, Maria E. Norm inflation for incompressible magneto-hydrodynamic system in $\dot{B}_{\infty}^{-1,\infty}$. Adv. Differential Equations 16 (2011), no. 7/8, 725--746. https://projecteuclid.org/euclid.ade/1355703204