TY - JOUR
T1 - Some Geometric Flows on Kahler Manifolds
JO - Journal of Partial Differential Equations
VL - 2
SP - 203
EP - 208
PY - 2010
DA - 2010/05
SN - 23
DO - http://doi.org/10.4208/jpde.v23.n2.6
UR - https://global-sci.org/intro/article_detail/jpde/5229.html
KW - KdV geometric flow
KW - conservation law
KW - local and global existence
AB - <p>We define a kind of KdV (Korteweg-de Vries) geometric flow for maps from a real line or a circle into a K<span style="font-size: 16px; line-height: 115%; font-family: arial, helvetica, sans-serif;">ä</span>hler manifold (N, J,h) with complex structure J and metric h as the generalization of the vortex filament dynamics from a real line or a circle. By using the geometric analysis, the existence of the Cauchy problems of the KdV geometric flows will be investigated in this note.</p>