A third-order conservation law for the Kirchhoff-Pokhozhaev equation
Analysis of PDEs
2025-12-16 v1
Abstract
We prove that the special Kirchhoff equation studied by Pokhozhaev admits a third-order conservation law. We further show that if the energy of the solution is sufficiently small, then the -norms of the derivatives up to third order of the solution remain uniformly bounded with respect to time.
Cite
@article{arxiv.2512.12380,
title = {A third-order conservation law for the Kirchhoff-Pokhozhaev equation},
author = {Chiara Boiti and Renato Manfrin},
journal= {arXiv preprint arXiv:2512.12380},
year = {2025}
}