University of Cambridge > > Partial Differential Equations seminar > Non-Newtonian fluids: applications of Orlicz spaces in the theory of nonlinear PDE

Non-Newtonian fluids: applications of Orlicz spaces in the theory of nonlinear PDE

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If you have a question about this talk, please contact Mikaela Iacobelli.

We are interested in the existence of solutions to strongly nonlinear partial differential equations. We concentrate mainly on problems which come from dynamics of non-Newtonian fluids of a nonstandard rheology, more general then of power-law type, and also on some abstract theory of elliptic and parabolic equations. In considered problems the nonlinear highest order term (stress tensor) is monotone and its behaviour – coercivity/growth condition – is given with help of some general convex function. In our research we would like to cover both cases: sub- and super-linear growth of nonlinearity (shear thickening and shear tinning fluids) as well its anisotropic and non-homogenous behaviour. Such a formulation requires a general framework for the function space setting, therefore we work with non-reflexive and non-separable anisotropic Orlicz and Musielak-Orlicz spaces. Within the presentation we would like to emphasise problems we have met during our studies, their reasons and methods which allow us to achieve existence results.

This talk is part of the Partial Differential Equations seminar series.

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