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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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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1355703204

Mathematical Reviews number (MathSciNet)
MR2829502

Zentralblatt MATH identifier
05953771

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

Citation

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.


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