Abstract
It has been shown that the Cauchy problem for the Fokas–Olver–Rosenau–Qiao equation is well-posed for initial data \(u_0\in H^s\), \(s>5/2\), with its data-to-solution map \(u_0\mapsto u\) being continuous but not uniformly continuous. This work further investigates the continuity properties of the solution map and shows that it is Hölder continuous in the \(H^r\) topology when \(0\le r<s\). The Hölder exponent is given explicitly and depends on both \(s\) and \(r\).
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Acknowledgments
This work was partially supported by a grant from the Simons Foundation (246116 to Alex Himonas) and an AMS-Simons Travel Grant to Dionyssios Mantzavinos. The authors would like to thank the referees of the paper for constructive comments that led to its improvement.
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Communicated by Darryl D. Holm.
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Himonas, A.A., Mantzavinos, D. Hölder Continuity for the Fokas–Olver–Rosenau–Qiao Equation. J Nonlinear Sci 24, 1105–1124 (2014). https://doi.org/10.1007/s00332-014-9212-y
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DOI: https://doi.org/10.1007/s00332-014-9212-y
Keywords
- Fokas
- Olver
- Rosenau
- Qiao equation
- Novikov equation
- Integrable equations
- Cubic nonlinearities
- Cauchy problem
- Sobolev spaces
- Well-posedness
- Hölder continuity