# One-parameter solutions of the Euler-Arnold equation on the contactomorphism group

@inproceedings{Preston2014OneparameterSO, title={One-parameter solutions of the Euler-Arnold equation on the contactomorphism group}, author={Stephen C. Preston and Alejandro Sarria}, year={2014} }

- Published 2014
DOI:10.3934/dcds.2015.35.2123

We study solutions of the equation gt − gtyy + 4g2 − 4ggyy = yggyyy − ygygyy, y ∈ R, which arises by considering solutions of the Euler-Arnold equation on a contactomorphism group when the stream function is of the form f (t, x, y, z) = zg(t, y). The equation is analogous to both the Camassa-Holm equation and the Proudman-Johnson equation. We write the equation as an ODE in a Banach space to establish local existence, and we describe conditions leading to global existence and conditions leading… CONTINUE READING

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