TY - JOUR
T1 - Global regularity of N-dimensional generalized MHD system with anisotropic dissipation and diffusion
AU - Yamazaki, Kazuo
N1 - Publisher Copyright:
© 2015 Elsevier Ltd.
PY - 2015/7/1
Y1 - 2015/7/1
N2 - Motivated by the anisotropic Navier-Stokes equations that have much applications in studying fluids in thin domains, in particular meteorology and oceanography, we study the magnetohydrodynamics system with generalized dissipation and diffusion, considering different exponents of the fractional Laplacians with logarithmic worsening applied to different directions and components of the solution vector fields. The results indicate that it is possible to regularize the flows by anisotropic dissipation, some components in various directions allowed to be below the critical exponents in the expense of others being above.
AB - Motivated by the anisotropic Navier-Stokes equations that have much applications in studying fluids in thin domains, in particular meteorology and oceanography, we study the magnetohydrodynamics system with generalized dissipation and diffusion, considering different exponents of the fractional Laplacians with logarithmic worsening applied to different directions and components of the solution vector fields. The results indicate that it is possible to regularize the flows by anisotropic dissipation, some components in various directions allowed to be below the critical exponents in the expense of others being above.
KW - Besov spaces
KW - Fractional Laplacian
KW - Global regularity
KW - Magnetohydrodynamics system
KW - Navier-Stokes equations
UR - http://www.scopus.com/inward/record.url?scp=84928799130&partnerID=8YFLogxK
U2 - 10.1016/j.na.2015.04.006
DO - 10.1016/j.na.2015.04.006
M3 - Article
AN - SCOPUS:84928799130
SN - 0362-546X
VL - 122
SP - 176
EP - 191
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
ER -