Local well-posedness for the fifth-order KdV equations on \(\mathbb{T}\). (English) Zbl 1339.35271
The purpose of this paper is to prove the local well-posedness of the fifth-order KdV equation for low regularity Sobolev initial data by the energy conservation laws. This is the second paper on the main theorem presented here, which states that a certain integrable fifth-order KdV on the torus has a unique solution. Therefore, in this paper, only proofs of nonlinear and energy estimates are given. The proof uses the Cauchy-Schwarz inequality and Sobolev embedding.
Reviewer: Thomas Ernst (Uppsala)
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
fifth-order KdV equation; local well-posedness; energy method; complete integrability; \(X^{s, b}\) space; modified energyReferences:
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