Generic regularity and Lipschitz metric for the Hunter-Saxton type equations (Q340354)

One- and two-component Hunter-Saxton model describing the propagation of weakly nonlinear orientation waves in a massive nematic liquid crystal, is studied for \((x,t)\in{\mathbb R}^+\times{\mathbb R}^+\). As it is known, finite time gradient blowup may happen in this system, so the solution flow is, in general, not Lipschitz continuous with respect to natural \(H^1\) distance. The authors study generic properties of conservative solutions and construct a Finsler type metric in which the solution flow is locally uniformly Lipschitz continuous.