A Remark on the Global Existence of a Third Order Dispersive Flow into Locally Hermitian Symmetric Spaces

作者：Onodera Eiji^*

来源：Communications in Partial Differential Equations, 2010, 35(6): 1130-1144.

DOI：10.1080/03605301003717134

• Dispersive flow
• Global existence
• Hirota equation
• Schrodinger map
• Vortex filament

We prove time-global existence of solutions to the initial value problem for a third order dispersive flow into compact locally Hermitian symmetric spaces. The equation under consideration generalizes two-sphere-valued completely integrable systems modeling the motion of vortex filament. Unlike one-dimensional Schrodinger maps, our third order equation is not completely integrable under the curvature condition on the target manifold in general. The idea of our proof is to exploit two conservation laws and an oalmost conserved quantityo which prevents the formation of a singularity in finite time.

• 出版日期2010