Blowup of solutions for compressible viscoelastic fluid

2025/09/05 by Boyaval, Sébastien, Wang, Na, Hu, Yuxi
#Analysis of PDEs (math.AP) #Classical Physics (physics.class-ph) #FOS: Mathematics #FOS: Physical sciences

paper · doi:10.48550/arxiv.2509.04924

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.

Citations

• Blow-up of solutions for relaxed compressible Navier-Stokes equations
• Globally analytical solutions of the compressible Oldroyd-B model without retardation
• Viscoelastic flows of Maxwell fluids with conservation laws
• On the formulation of rheological equations of state

Related

• On blowup of classical solutions to the compressible Navier-Stokes equations
• Remarks on Blow-up of Smooth Solutions to the Compressible Fluid with Constant and Degenerate Viscosities
• Local Strong Solution to the Compressible Viscoelastic Fluid with Large Data
• Formation of singularity for compressible viscoelasticity
• On blow-up to the one-dimensional Navier-Stokes equations with degenerate viscosity and vacuum