Advances in Differential Equations

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

Mimi Dai, Jie Qing, and Maria E. Schonbek

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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

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

First available in Project Euclid: 17 December 2012

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 35Q35: PDEs in connection with fluid mechanics


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.

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