Uniqueness of dissipative solutions for the Camassa-Holm equation
Peer reviewed, Journal article
Published version
Permanent lenke
https://hdl.handle.net/11250/3148874Utgivelsesdato
2024Metadata
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- Institutt for matematiske fag [2527]
- Publikasjoner fra CRIStin - NTNU [38679]
Originalversjon
Journal of Differential Equations. 2024, 412 474-528. https://doi.org/10.1016/j.jde.2024.08.036Sammendrag
We show that the Cauchy problem for the Camassa–Holm equation has a unique, global, weak, and dissipative solution for any initial data u0 ∈H1(R), such that u0,x is bounded from above almost everywhere. In particular, we establish a one-to-one correspondence between the properties specific to the dissipative solutions and a solution operator associating to each initial data exactly one solution.