Corpus ID: 118393495

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

@article{Benvenutti2014ExistenceAS,
  title={Existence and stability of global large strong solutions for the Hall-MHD system},
  author={M. J. Benvenutti and L. Ferreira},
  journal={arXiv: Analysis of PDEs},
  year={2014}
}
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. 
24 Citations
Global Existence and Optimal Decay Rates of Solutions for Compressible Hall-MHD Equations
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References

SHOWING 1-10 OF 47 REFERENCES
THE GLOBAL L2 STABILITY OF SOLUTIONS TO THREE DIMENSIONAL MHD EQUATIONS
On the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics
Global stability of large solutions to the 3D Navier-Stokes equations
Well-posedness for Hall-magnetohydrodynamics
Navier–Stokes equations, stability and minimal perturbations of global solutions
On the stability of global solutions to Navier–Stokes equations in the space
On the stability of global solutions to the 3D Boussinesq system
Regularity Criteria for the Generalized MHD Equations
...
1
2
3
4
5
...