In this paper, we deal with the 212 dimensional Hall MHD by taking the velocity field u and the magnetic field B of the form u(t, x, y) = (∇ ⊥ϕ(t, x, y) , W(t, x, y)) and B(t, x, y) = (∇ ⊥ψ(t, x, y) , Z(t, x, y)). We begin with the Hall equations (without the effect of the fluid part). In this case, we provide several results such as the long time behavior of weak solutions, weak-strong uniqueness, the existence of local and global in time strong solutions, decay rates of (ψ, Z) , the asymptotic profiles of (ψ, Z) , and the perturbation around harmonic functions. In the presence of the fluid field, the results, by comparison, fall short of the previous ones in the absence of the fluid part and we show the existence of local and global in time strong solutions.
|Journal||Journal of Mathematical Fluid Mechanics|
|Publication status||Published - 2023 May|
Bibliographical noteFunding Information:
The authors acknowledge the referees for his/her valuable comments and suggestions that highly improved the manuscript. H.B. and R.K acknowledge Prof. Danchin for letting us know his recent paper in . H.B. was supported by NRF-2018R1D1A1B07049015. K.K. was supported by NRF-2019R1A2C1084685 and NRF-20151009350.
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
All Science Journal Classification (ASJC) codes
- Mathematical Physics
- Condensed Matter Physics
- Computational Mathematics
- Applied Mathematics