TY - JOUR
T1 - Remarks on the global regularity of the two-dimensional magnetohydrodynamics system with zero dissipation
AU - Yamazaki, Kazuo
PY - 2014
Y1 - 2014
N2 - We study the two-dimensional magnetohydrodynamics system with generalized dissipation and diffusion in terms of fractional Laplacians. It is known that the classical magnetohydrodynamics system with full Laplacians in both dissipation and diffusion terms admits a unique global strong solution pair. Making use of the special structure of the system in the two-dimensional case, we show in particular that the solution pair remains smooth when we have zero dissipation but only magnetic diffusion with its power of the fractional Laplacian β>32.
AB - We study the two-dimensional magnetohydrodynamics system with generalized dissipation and diffusion in terms of fractional Laplacians. It is known that the classical magnetohydrodynamics system with full Laplacians in both dissipation and diffusion terms admits a unique global strong solution pair. Making use of the special structure of the system in the two-dimensional case, we show in particular that the solution pair remains smooth when we have zero dissipation but only magnetic diffusion with its power of the fractional Laplacian β>32.
KW - Euler equations
KW - Global regularity
KW - Littlewood-Paley theory
KW - Magnetohydrodynamics system
KW - Navier-Stokes system
UR - http://www.scopus.com/inward/record.url?scp=84884198854&partnerID=8YFLogxK
U2 - 10.1016/j.na.2013.08.020
DO - 10.1016/j.na.2013.08.020
M3 - Article
AN - SCOPUS:84884198854
SN - 0362-546X
VL - 94
SP - 194
EP - 205
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -