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

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:503

Article

Onodera, Eiji¹  Yamasaki, Haruka² 

[1] Kochi Univ, Fac Sci & Technol, Dept Math, Kochi 7808520, Japan

[2] Kochi Dist Court, Kochi, Japan

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

DOI  :  10.1016/j.jmaa.2021.125297

来源: Elsevier

【 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.

【 授权许可】

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