Analyticity of the Cauchy problem for an integrable evolution equation
AA Himonas, G Misiołek - Mathematische Annalen, 2003 - Springer
AA Himonas, G Misiołek
Mathematische Annalen, 2003•Springer… In this paper we consider the periodic Cauchy problem for the Camassa-Holm equation with
analytic initial data and prove that its solutions are analytic in both variables, globally in space
and locally in time. … We thankYann Brenier and Sasha Shnirelman for interesting conversations
which stimulated our interest in the problem of analytic regularity for the CH equation. We also
thank the referee for suggestions to improve the presentation of this paper. … Sharp estimates
for analytic pseudodifferential operators and application to Cauchy problems. J. Diff. …
analytic initial data and prove that its solutions are analytic in both variables, globally in space
and locally in time. … We thankYann Brenier and Sasha Shnirelman for interesting conversations
which stimulated our interest in the problem of analytic regularity for the CH equation. We also
thank the referee for suggestions to improve the presentation of this paper. … Sharp estimates
for analytic pseudodifferential operators and application to Cauchy problems. J. Diff. …
Abstract
In this paper we consider the periodic Cauchy problem for the Camassa-Holm equation with analytic initial data and prove that its solutions are analytic in both variables, globally in space and locally in time.
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