6533b829fe1ef96bd1289739

RESEARCH PRODUCT

Global existence and uniqueness result for the diffusive Peterlin viscoelastic model

Hana MizerováMária Lukáčová Medvid’ováŠáRka Nečasová

subject

Nonlinear systemApplied MathematicsWeak solutionMathematical analysisCompressibilityTime evolutionUniquenessTensorSpace (mathematics)AnalysisViscoelasticityMathematics

description

Abstract The aim of this paper is to present the existence and uniqueness result for the diffusive Peterlin viscoelastic model describing the unsteady behaviour of some incompressible polymeric fluids. The polymers are treated as two beads connected by a nonlinear spring. The Peterlin approximation of the spring force is used to derive the equation for the conformation tensor. The latter is the time evolution equation with spatial diffusion of the conformation tensor. Using the energy estimates we prove global in time existence of a weak solution in two space dimensions. We are also able to show the regularity and consequently the uniqueness of the weak solution.

yearjournalcountryeditionlanguage
2015-06-01Nonlinear Analysis: Theory, Methods & Applications
https://doi.org/10.1016/j.na.2015.03.001