Hölder continuity of the solution map for the Novikov equation
AA Himonas, J Holmes - Journal of Mathematical Physics, 2013 - pubs.aip.org
The Novikov equation (NE) has been discovered recently as a new integrable equation with
cubic nonlinearities that is similar to the Camassa-Holm and Degasperis-Procesi equations,
which have quadratic nonlinearities. NE is well-posed in Sobolev spaces H s on both the
line and the circle for s> 3/2, in the sense of Hadamard, and its data-to-solution map is
continuous but not uniformly continuous. This work studies the continuity properties of NE
further. For initial data in H s, s> 3/2, it is shown that the solution map for NE is Hölder …
cubic nonlinearities that is similar to the Camassa-Holm and Degasperis-Procesi equations,
which have quadratic nonlinearities. NE is well-posed in Sobolev spaces H s on both the
line and the circle for s> 3/2, in the sense of Hadamard, and its data-to-solution map is
continuous but not uniformly continuous. This work studies the continuity properties of NE
further. For initial data in H s, s> 3/2, it is shown that the solution map for NE is Hölder …
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