[PDF][PDF] Non-uniform continuity in of the solution map of the CH equation
AA Himonas, G Misiołek, G Ponce - 2007 - projecteuclid.org
AA Himonas, G Misiołek, G Ponce
2007•projecteuclid.orgWe show that the solution map of the Camassa-Holm equation is not uniformly continuous in
the initial data in the Sobolev space of order one on the torus and the real line. The proof
relies on a construction of non-smooth travelling wave solutions. We also extend to all Hs an
earlier result known to hold for peakons.
the initial data in the Sobolev space of order one on the torus and the real line. The proof
relies on a construction of non-smooth travelling wave solutions. We also extend to all Hs an
earlier result known to hold for peakons.
Abstract
We show that the solution map of the Camassa-Holm equation is not uniformly continuous in the initial data in the Sobolev space of order one on the torus and the real line. The proof relies on a construction of non-smooth travelling wave solutions. We also extend to all Hs an earlier result known to hold for peakons.
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