LAUSR

Abstract The Hunter–Saxton equation determines a flow of conservative solutions taking values in the space H 1 ( R + ) . However, the solution typically includes finite time gradient blowups, which make the solution flow not continuous w.r.t. the natural H 1 distance. The aim of this paper is to first study the generic properties of conservative solutions of some initial boundary value problems to the Hunter–Saxton type equations. Then using these properties, we give a new way to construct a Finsler type metric which renders the flow uniformly Lipschitz continuous on bounded subsets of H 1 ( R + ) .