TY - JOUR
T1 - On the three-dimensional magnetohydrodynamics system in scaling-invariant spaces
AU - Yamazaki, Kazuo
N1 - Publisher Copyright:
© 2015 Elsevier Masson SAS
PY - 2016/6/1
Y1 - 2016/6/1
N2 - We study the criterion for the velocity and magnetic vector fields that solve the three-dimensional magnetohydrodynamics system, given any initial data sufficiently smooth, to experience a finite-time blowup. Following the work of Chemin and Zhang [12] and making use of the structure of the system, we obtain a criterion that is imposed on the magnetic vector field and only one of the three components of the velocity vector field, both in scaling-invariant spaces.
AB - We study the criterion for the velocity and magnetic vector fields that solve the three-dimensional magnetohydrodynamics system, given any initial data sufficiently smooth, to experience a finite-time blowup. Following the work of Chemin and Zhang [12] and making use of the structure of the system, we obtain a criterion that is imposed on the magnetic vector field and only one of the three components of the velocity vector field, both in scaling-invariant spaces.
KW - Anisotropic Littlewood–Paley theory
KW - Global regularity
KW - Magnetohydrodynamics system
KW - Navier–Stokes equations
UR - http://www.scopus.com/inward/record.url?scp=84940766557&partnerID=8YFLogxK
U2 - 10.1016/j.bulsci.2015.08.003
DO - 10.1016/j.bulsci.2015.08.003
M3 - Article
AN - SCOPUS:84940766557
SN - 0007-4497
VL - 140
SP - 575
EP - 614
JO - Bulletin des Sciences Mathematiques
JF - Bulletin des Sciences Mathematiques
IS - 5
ER -