TY - JOUR
T1 - A Remark on the Two-Dimensional Magneto-Hydrodynamics-Alpha System
AU - Yamazaki, Kazuo
N1 - Publisher Copyright:
© 2016, Springer International Publishing.
PY - 2016/9/1
Y1 - 2016/9/1
N2 - We study the generalized magneto-hydrodynamics-α system in two dimensional space with fractional Laplacians in the dissipative and diffusive terms. We show that the solution pair of velocity and magnetic fields preserves their initial regularity in all cases when the powers add up to one. This settles the global regularity issue in the general case which was remarked by the authors in Zhao and Zhu (Appl Math Lett 29:26–29, 2014) to be a problem.
AB - We study the generalized magneto-hydrodynamics-α system in two dimensional space with fractional Laplacians in the dissipative and diffusive terms. We show that the solution pair of velocity and magnetic fields preserves their initial regularity in all cases when the powers add up to one. This settles the global regularity issue in the general case which was remarked by the authors in Zhao and Zhu (Appl Math Lett 29:26–29, 2014) to be a problem.
KW - Magneto-hydrodynamics system
KW - Navier–Stokes equations
KW - fractional Laplacians
KW - global regularity
KW - α-regularization
UR - http://www.scopus.com/inward/record.url?scp=84983036004&partnerID=8YFLogxK
U2 - 10.1007/s00021-016-0259-4
DO - 10.1007/s00021-016-0259-4
M3 - Article
AN - SCOPUS:84983036004
SN - 1422-6928
VL - 18
SP - 609
EP - 623
JO - Journal of Mathematical Fluid Mechanics
JF - Journal of Mathematical Fluid Mechanics
IS - 3
ER -