English

On blow-up shock waves for a nonlinear PDE associated with Euler equations

Analysis of PDEs 2009-02-12 v1

Abstract

A second-order PDE is derived from Euler's equaitons under certain assumptions. It is shown that this PDE admits shock and rarefaction waves, and that a single point gradient blow-up admits a unique similarity extension after blow-up that settles uniqueness/entropy issues for such equations.

Keywords

Cite

@article{arxiv.0902.1840,
  title  = {On blow-up shock waves for a nonlinear PDE associated with Euler equations},
  author = {V. A. Galaktionov},
  journal= {arXiv preprint arXiv:0902.1840},
  year   = {2009}
}

Comments

16 pages, 8 figures

R2 v1 2026-06-21T12:10:07.332Z