Orbital stability of undercompressive viscous shock waves under $L^1\cap H^4$ perturbation

By the use of a new vertical estimate introduced by the authors in the context of relaxation shocks for shallow water flow, we both simplify and extend the basic $L^1\cap H^3$ stability results of Mascia and Zumbrun for viscous shock waves, in particular extending their results for Lax waves to the undercompressive case.