Pseudo-monotone operator theory for electro-rheological fluids
A talk in the BI.discrete series by
Alex Kaltenbach from Freiburg
| Abstract: | We consider a model describing the unsteady motion of an
incompressible, electro-rheological fluid. Due to the
time-space-dependence of the power-law index, the analytical treatment
of this system is involved. Standard results like a Poincare or a Korn
inequality are not available. Introducing natural energy spaces and
constructing suitable smoothing methods, we establish the validity of a
formula of integration-by-parts which allows to extend the classical
theory of pseudo-monotone operators to the framework of variable
Bochner-Lebesgue spaces. This leads to generalised notions of
pseudo-monotonicity and coercivity, the so-called Bochner
pseudo-monotonicity and Bochner coercivity. With the aid of these
notions and the established formula of integration-by-parts it is
possible to prove an abstract existence result which immediately
implies the weak solvability of the model describing the unsteady
motion of an incompressible, electro-rheological fluid. Within the CRC this talk is associated to the project(s): A7 |