Blowup of solutions for compressible viscoelastic fluid
Analysis of PDEs
2025-09-08 v1 Classical Physics
Abstract
We prove finite-time blowup of classical solutions for the compressible Upper Convective Maxwell (UCM) viscoelastic fluid system. By establishing a key energy identity and adapting Sideris' method for compressible flows, we derive a Riccati-type inequality for a momentum functional. For initial data with compactly supported perturbations satisfying a sufficiently large condition, all classical solutions lose regularity in finite time. This constitutes the first rigorous blowup result for multidimensional compressible viscoelastic fluids.
Keywords
Cite
@article{arxiv.2509.04924,
title = {Blowup of solutions for compressible viscoelastic fluid},
author = {Sébastien Boyaval and Na Wang and Yuxi Hu},
journal= {arXiv preprint arXiv:2509.04924},
year = {2025}
}