Abstract
This article is devoted to studying the initial value problem for a third-order dispersive equation for closed curves into Kähler manifolds. This equation is a geometric generalization of a two-sphere valued system modeling the motion of vortex filament. We prove the local existence theorem by using geometric analysis and classical energy method.
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The author is supported by the JSPS Research Fellowships for Young Scientists and the JSPS Grant-in-Aid for Scientific Research No. 19⋅3304.
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Onodera, E. A Third-Order Dispersive Flow for Closed Curves into Kähler Manifolds. J Geom Anal 18, 889–918 (2008). https://doi.org/10.1007/s12220-008-9023-1
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DOI: https://doi.org/10.1007/s12220-008-9023-1