A third order dispersive flow for closed curves into almost Hermitian manifolds

Access this Article

Search this Article

Abstract

We discuss a short-time existence theorem of solutions to the initial value problem for a third order dispersive flow for closed curves into a compact almost Hermitian manifold. Our equations geometrically generalize a physical model describing the motion of vortex filament. The classical energy method cannot work for this problem since the almost complex structure of the target manifold is not supposed to be parallel with respect to the Levi-Civita connection. In other words, a loss of one derivative arises from the covariant derivative of the almost complex structure. To overcome this difficulty, we introduce a bounded pseudodifferential operator acting on sections of the pullback bundle, and eliminate the loss of one derivative from the partial differential equation of the dispersive flow.

Journal

  • Journal of Functional Analysis

    Journal of Functional Analysis 257(2), 388-404, 2009-04-22

    Elsevier

Codes

  • NII Article ID (NAID)
    120001224291
  • NII NACSIS-CAT ID (NCID)
    AA00252370
  • Text Lang
    ENG
  • Article Type
    journal article
  • ISSN
    0022-1236
  • Data Source
    IR 
Page Top