On the Well-Posedness of the Hall-Magnetohydrodynamics with the Ion-Slip Effect
| Autor: | Byungsoo Moon, Hyung Ju Hwang, Woo Jin Han |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Physics
Applied Mathematics 010102 general mathematics Mathematical analysis Slip (materials science) Condensed Matter Physics 01 natural sciences Ion 010101 applied mathematics Computational Mathematics Physics::Plasma Physics Inviscid flow Bounded function Boundary value problem 0101 mathematics Magnetohydrodynamics Mathematical Physics Well posedness |
| Zdroj: | Journal of Mathematical Fluid Mechanics. 21 |
| ISSN: | 1422-6952 1422-6928 |
| DOI: | 10.1007/s00021-019-0455-0 |
| Popis: | The existence of global weak solutions is established to the magnetohydrodynamics (MHD) equations with Hall and ion-slip effects in a bounded domain, which coincide with the Hall-MHD equations with and without ion-slip effect for the complementary choices of the parameter $$\gamma =1$$ and $$\gamma =0$$, respectively. It is also shown that a similar result holds in the whole space. Moreover, the local existence of a unique strong solution and the global well-posedness for small initial data are obtained to the Hall-MHD equations with and without ion-slip effect in both a cubic bounded domain with a flat boundary condition and the whole space. Furthermore, the vanishing viscosity limit to inviscid MHD equations is studied without the ion-slip effect ($$\gamma =0$$) in the cubic bounded domain with the flat boundary condition and with the ion-slip effect ($$\gamma =1$$) in the whole space, respectively. |
| Databáze: | OpenAIRE |
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