TY - JOUR
T1 - Quantitative equipartition of the ginzburg-landau energy with applications
AU - Kurzke, Matthias
AU - Spirn, Daniel
PY - 2010
Y1 - 2010
N2 - We study the Ginzburg-Landau energy of a single vortex and prove a quantitative estimate for the anisotropy of the stress-energy tensor. In particular we establish an asymptotic rate of equipartitioning of the energy along each direction. By means of an explicit example, this rate is shown to be optimal up to a constant. The result has applications in the study of the nonlinear wave equation and Ginzburg-Landau heat flow.
AB - We study the Ginzburg-Landau energy of a single vortex and prove a quantitative estimate for the anisotropy of the stress-energy tensor. In particular we establish an asymptotic rate of equipartitioning of the energy along each direction. By means of an explicit example, this rate is shown to be optimal up to a constant. The result has applications in the study of the nonlinear wave equation and Ginzburg-Landau heat flow.
KW - Finite epsilon estimates
KW - Ginzburg-Landau energy
KW - Ginzburg-Landau vortices
KW - Stress-energy tensor
UR - http://www.scopus.com/inward/record.url?scp=84856479908&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84856479908&partnerID=8YFLogxK
U2 - 10.1512/iumj.2010.59.4565
DO - 10.1512/iumj.2010.59.4565
M3 - Article
AN - SCOPUS:84856479908
SN - 0022-2518
VL - 59
SP - 2013
EP - 2028
JO - Indiana University Mathematics Journal
JF - Indiana University Mathematics Journal
IS - 6
ER -