On classical solutions for some Oldroyd-B model of viscoelastic fluids

Abstract: This talk is devoted to the analysis of an Oldroyd-B system of PDEs which models the evolution of certain viscoelastic fluids. A particular emphasis is spent on the so called "corotational" model. We are interested in the well-posedness theory of classical solutions. We show in a bidimensional setting that, without any restriction on the initial data, the solutions exist globally in time and they are unique.

This result is due to the particular structure of the system which allows to propagate high regularities of the solutions, in particular a Lipschitz regularity of the velocity field. A specific toolbox of Fourier Analysis is presented to address the mentioned result.

general mathematics

Audience: researchers in the topic

( paper )

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