A fifth-order dispersive partial differential equation for curve flow on the sphere

[摘要] 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 onedimensional 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. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-11-01

[关键词] Nonlinear dispersive partial;differential equation;Local existence and uniqueness;Loss of derivative;Energy method;Gauge transformation