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arXiv · 2509.04924

Blowup of solutions for compressible viscoelastic fluid

Sébastien Boyaval·Na Wang·Yuxi Hu
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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.

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Sébastien Boyaval, Na Wang, Yuxi Hu. 2025-09-05. Blowup of solutions for compressible viscoelastic fluid. https://arxiv.org/abs/2509.04924

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