TY - JOUR
T1 - Regularity results on the Leray-alpha magnetohydrodynamics systems
AU - Kc, Durga
AU - Yamazaki, Kazuo
N1 - Publisher Copyright:
© 2016 Elsevier Ltd. All rights reserved.
PY - 2016/12/1
Y1 - 2016/12/1
N2 - We study certain generalized Leray-alpha magnetohydrodynamics systems. We show that the solution pairs of velocity and magnetic fields to this system in two-dimension preserve their initial regularity in two cases: dissipation logarithmically weaker than a full Laplacian and zero diffusion, zero dissipation and diffusion logarithmically weaker than a full Laplacian. These results extend previous results in Zhou and Fan (2011). Moreover, we show that for a certain three-dimensional Leray-alpha magnetohydrodynamics system, sufficient condition of regularity may be reduced to a horizontal gradient or a partial derivative in just one direction of the magnetic field, reducing components from the results in Fan and Ozawa (2009).
AB - We study certain generalized Leray-alpha magnetohydrodynamics systems. We show that the solution pairs of velocity and magnetic fields to this system in two-dimension preserve their initial regularity in two cases: dissipation logarithmically weaker than a full Laplacian and zero diffusion, zero dissipation and diffusion logarithmically weaker than a full Laplacian. These results extend previous results in Zhou and Fan (2011). Moreover, we show that for a certain three-dimensional Leray-alpha magnetohydrodynamics system, sufficient condition of regularity may be reduced to a horizontal gradient or a partial derivative in just one direction of the magnetic field, reducing components from the results in Fan and Ozawa (2009).
KW - Besov spaces
KW - Magnetohydrodynamics system
KW - Navier-Stokes equations
KW - Regularity
UR - http://www.scopus.com/inward/record.url?scp=84966280485&partnerID=8YFLogxK
U2 - 10.1016/j.nonrwa.2016.04.006
DO - 10.1016/j.nonrwa.2016.04.006
M3 - Article
AN - SCOPUS:84966280485
SN - 1468-1218
VL - 32
SP - 178
EP - 197
JO - Nonlinear Analysis: Real World Applications
JF - Nonlinear Analysis: Real World Applications
ER -