Global-in-Time Stability of 2D MHD Boundary Layer in the Prandtl--Hartmann Regime

Feng Xie Tong Yang

Fluid Dynamics and Shock Waves mathscidoc:1912.431008

SIAM Journal on Mathematical Analysis, 50, (6), 5749-5760, 2018.11
In this paper, we prove the global existence of solutions with analytic regularity to the 2D magnetohydrodynamic (MHD) boundary layer equations in the mixed Prandtl and Hartmann regime derived by formal multiscale expansion in [D. Gerard-Varet and M. Prestipino, <i>Z. Angew. Math. Phys.</i>, 68 (2017), 76]. The analysis shows that the combined effect of the magnetic diffusivity and transverse magnetic field on the boundary leads to a linear damping on the tangential velocity field near the boundary. And this damping effect yields the global-in-time analytic norm estimate in the tangential space variable on the perturbation of the classical steady Hartmann profile.
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@inproceedings{feng2018global-in-time,
  title={Global-in-Time Stability of 2D MHD Boundary Layer in the Prandtl--Hartmann Regime},
  author={Feng Xie, and Tong Yang},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211207648471572},
  booktitle={SIAM Journal on Mathematical Analysis},
  volume={50},
  number={6},
  pages={5749-5760},
  year={2018},
}
Feng Xie, and Tong Yang. Global-in-Time Stability of 2D MHD Boundary Layer in the Prandtl--Hartmann Regime. 2018. Vol. 50. In SIAM Journal on Mathematical Analysis. pp.5749-5760. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224211207648471572.
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