What is it about?
Viscoelastic fluid flow can be thought of as a solution to a system of differential equations that generalize the famous Navier-Stokes equations. By making some natural constitutive choices for the internal energy of the fluid, we are able to guarantee that the system indeed always admits a solution.
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Why is it important?
Viscoelastic fluids are ubiquitous in our everyday lives: from medicine to applications in industry. In addition to usual viscous properties of a fluid, viscoleastic fluids can also store and release elastic energy, much like a rubber band or a spring. This leads to many unexpected phenomena and rather complex mathematical description. Finding feasible mathematical and physical models for such fluids is thus a very challenging task that, however, has an immediate impact on designing accurate computer simulations of viscoelastic fluid flow.
Perspectives
This work shows that including a nonlinearity in a model at the right place can actually help in the analysis, without changing the underlying physics too much. This idea is here applied to the (in)famous Navier-Stokes-Oldroyd-B model.
PhD Michal Bathory
Charles University
Read the Original
This page is a summary of: Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion, Advances in Nonlinear Analysis, September 2020, De Gruyter,
DOI: 10.1515/anona-2020-0144.
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