## Differential and Integral Equations

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

#### Abstract

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

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

Dates
First available in Project Euclid: 14 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.die/1465912613

Mathematical Reviews number (MathSciNet)
MR3513590

Zentralblatt MATH identifier
06644058

#### Citation

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.