Differential and Integral Equations

Existence and stability of global large strong solutions for the Hall-MHD system

Maicon J. Benvenutti and Lucas C.F. Ferreira

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We consider the 3D incompressible Hall-MHD system and prove a stability theorem for global large solutions under a suitable integrable hypothesis in which one of the parcels is linked to the Hall term. As a byproduct, a class of global strong solutions is obtained with large velocities and small initial magnetic fields. Moreover, we prove the local-in-time well-posedness of $H^{2} $-strong solutions which improves previous regularity conditions on initial data.

Article information

Differential Integral Equations, Volume 29, Number 9/10 (2016), 977-1000.

First available in Project Euclid: 14 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35Q35: PDEs in connection with fluid mechanics 76D03: Existence, uniqueness, and regularity theory [See also 35Q30] 35B35: Stability 76E25: Stability and instability of magnetohydrodynamic and electrohydrodynamic flows 76W05: Magnetohydrodynamics and electrohydrodynamics


Benvenutti, Maicon J.; Ferreira, Lucas C.F. Existence and stability of global large strong solutions for the Hall-MHD system. Differential Integral Equations 29 (2016), no. 9/10, 977--1000. https://projecteuclid.org/euclid.die/1465912613

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