One-sided Hölder regularity of global weak solutions of negative order dispersive equations

Abstract

We prove global existence, uniqueness and stability of entropy solutions with L2 initial data for a general family of negative order dispersive equations. These weak solutions are found to satisfy one-sided Hölder conditions whose coefficients decay in time. The latter result controls the height of solutions and further provides a way to bound the maximal lifespan of classical solutions from their initial data.