The r-Hunter-Saxton equation, smooth and singular solutions and their approximation

Abstract

In this work we introduce the r-Hunter-Saxton equation, a generalisation of the Hunter-Saxton equation arising as extremals of an action principle posed in L_r. We characterise solutions to the Cauchy problem, quantifying the blow-up time and studying various symmetry reductions. We construct piecewise linear functions and show that they are weak solutions to the r-Hunter-Saxton equation.

arXiv commentRevised after referee comments

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Cited by in corpus (3)

• A geometric view on the generalized Proudman-Johnson and $r$-Hunter-Saxton equations
• The $L^p$-Fisher-Rao metric and Amari-Cencov $\alpha$-connections
• Can we run to infinity? The diameter of the diffeomorphism group with respect to right-invariant Sobolev metrics