Abstract
In this paper we consider the Cauchy problem for a higher order modified Camassa–Holm equation. By using the Fourier restriction norm method introduced by Bourgain, we establish the local well-posedness for the initial data in the H s(R) with \({s > -n+\frac{5}{4},\,n\in {\bf N}^{+}.}\) As a consequence of the conservation of the energy \({{||u||_{H^{1}(R)},}}\) we have the global well-posedness for the initial data in H 1(R).
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Li, Y., Yan, W. & Yang, X. Well-posedness of a higher order modified Camassa–Holm equation in spaces of low regularity. J. Evol. Equ. 10, 465–486 (2010). https://doi.org/10.1007/s00028-010-0057-z
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DOI: https://doi.org/10.1007/s00028-010-0057-z