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 $L^2\cap L^{\infty }$ initial data for a general family of negative order dispersive equations. It is further demonstrated that this solution concept extends in a unique continuous manner to all $L^2$ initial data. 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.

arXiv comment46 pages

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• Wave breaking for the generalized Fornberg-Whitham equation