Oleinik type estimates for the Ostrovsky-Hunter eequation
Analysis of PDEs
2016-10-05 v1
Abstract
The Ostrovsky-Hunter equation provides a model for small-amplitude long waves in a rotating fluid of finite depth. It is a nonlinear evolution equation. In this paper we study the well-posedness for the Cauchy problem associated to this equation within a class of bounded discontinuous solutions. We show that we can replace the Kruzkov-type entropy inequalities by an Oleinik-type estimate and prove uniqueness via a nonlocal adjoint problem. An implication is that a shock wave in an entropy weak solution to the Ostrovsky-Hunter equation is admissible only if it jumps down in value (like the inviscid Burgers equation).
Cite
@article{arxiv.1403.2349,
title = {Oleinik type estimates for the Ostrovsky-Hunter eequation},
author = {G. M. Coclite and L. di Ruvo},
journal= {arXiv preprint arXiv:1403.2349},
year = {2016}
}