On Dissipative Solutions to a System Arising in Viscoelasticity
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We consider a model for an incompressible visoelastic fluid. It consists of the Navier–Stokes equations involving an elastic term in the stress tensor and a transport equation for the evolution of the deformation gradient. The novel feature of the paper is the introduction of the notion of a dissipative solution and its analysis. We show that dissipative solutions exist globally in time for arbitrary finite energy initial data and that a dissipative solution and a strong solution emanating from the same initial data coincide as long as the latter exists.
KeywordsIncompressible vicoelastic system Dissipative solution Existence Weak-strong uniqueness
Mathematics Subject ClassificationPrimary 35Q35 35Q74 Secondary 76A10
The research leading to these results was supported by DFG grant SCHL 1706/4-1.
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Conflict of interest
The author declares that he has no conflict of interest.
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