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Regularity criteria for 3D Hall-MHD equations.
- Source :
-
Zeitschrift für Angewandte Mathematik und Physik (ZAMP) . Dec2022, Vol. 73 Issue 6, p1-20. 20p. - Publication Year :
- 2022
-
Abstract
- A challenging open problem in the 3D Hall-MHD theory is to ask whether or not the global weak solutions are smooth. In this paper, we prove that a weak solution is smooth if the diagonal part of the velocity gradient tensor and the non-diagonal part of the magnetic gradient tensor satisfy Ladyzhenskaya–Prodi–Serrin-type conditions. It is physically interesting since the diagonal part of a gradient tensor is related to the deformation while the non-diagonal part is related to the rotation. Moreover, our main theorems improve significantly a criterion in Ye (Comput Math Appl 70(8):2137–2154, 2015) where all entries of the velocity gradient tensor and the magnetic gradient tensor are needed. [ABSTRACT FROM AUTHOR]
- Subjects :
- *EQUATIONS
*ROTATIONAL motion
*VELOCITY
*MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00442275
- Volume :
- 73
- Issue :
- 6
- Database :
- Academic Search Index
- Journal :
- Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
- Publication Type :
- Academic Journal
- Accession number :
- 160255108
- Full Text :
- https://doi.org/10.1007/s00033-022-01883-w