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A fifth-order dispersive partial differential equation for curve flow on the sphere 小野寺, 栄治 山﨑, 遥 open access © 2021 Elsevier Inc. All rights reserved. nonlinear dispersive partial differential equation local existence and uniqueness loss of derivative energy method gauge transformation The initial value problem for a fifth-order nonlinear dispersive partial differential equation describing the curve flow on the sphere is considered. A typical example of the equation arises in a hierarchy of completely integrable systems containing one-dimensional classical Heisenberg ferromagnetic spin model. This paper establishes the local existence and uniqueness of a solution to the initial value problem under the periodic boundary condition. The proof is based on the energy method combined with a kind of gauge transformation to overcome the difficulty of a loss of derivative. Elsevier 2021-11-01 eng journal article AM http://hdl.handle.net/10126/0002000210 https://kochi.repo.nii.ac.jp/records/2000210 https://doi.org/10.1016/j.jmaa.2021.125297 0022-247X Journal of Mathematical Analysis and Applications 503 1 125297 https://kochi.repo.nii.ac.jp/record/2000210/files/JMMA_503-1-125297.pdf application/pdf 168 KB 2024-04-19