TY - JOUR
T1 - Non-uniform decay of MHD equations with and without magnetic diffusion
AU - Agapito, Rubén
AU - Schonbek, Maria
PY - 2007/11
Y1 - 2007/11
N2 - We consider the long time behavior of solutions to the magnetohydrodynamics equations in two and three spatial dimensions. It is shown that in the absence of magnetic diffusion, if strong bounded solutions were to exist their energy cannot present any asymptotic oscillatory behavior, the diffusivity of the velocity is enough to prevent such oscillations. When magnetic diffusion is present and the data is only in L2, it is shown that the solutions decay to zero without a rate, and this nonuniform decay is optimal.
AB - We consider the long time behavior of solutions to the magnetohydrodynamics equations in two and three spatial dimensions. It is shown that in the absence of magnetic diffusion, if strong bounded solutions were to exist their energy cannot present any asymptotic oscillatory behavior, the diffusivity of the velocity is enough to prevent such oscillations. When magnetic diffusion is present and the data is only in L2, it is shown that the solutions decay to zero without a rate, and this nonuniform decay is optimal.
KW - Decay rates
KW - Magneto-hydrodynamics
UR - http://www.scopus.com/inward/record.url?scp=36448967196&partnerID=8YFLogxK
U2 - 10.1080/03605300701318658
DO - 10.1080/03605300701318658
M3 - Article
AN - SCOPUS:36448967196
SN - 0360-5302
VL - 32
SP - 1791
EP - 1812
JO - Communications in Partial Differential Equations
JF - Communications in Partial Differential Equations
IS - 11
ER -