Formation of singularity for compressible viscoelasticity

Abstract

The formation of singularity and breakdown of classical solutions to the three-dimensional compressible viscoelasticity and inviscid elasticity are considered. For the compressible inviscid elastic fluids, the finite-time formation of singularity in classical solutions is proved for certain initial data. For the compressible viscoelastic fluids, a criterion in term of the temporal integral of the velocity gradient is obtained for the breakdown of smooth solutions.

References in corpus (2)

• A Blow-Up Criterion for Classical Solutions to the Compressible Navier-Stokes Equations
• Global Existence with Small Initial Data for Three-Dimensional Incompressible Isotropic Viscoelastic Materials

Cited by in corpus (2)

• A blow-up criterion for 3-D compressible visco-elasticity
• Global solution in critical spaces to the compressible Oldroyd-B model with non-small coupling parameter