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Mittwoch, 1.5.13, 03:00-04:00, Raum 414, Eckerstr. 1
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On the existence of a local pressure for general systems of incompressible viscous fluids
Dienstag, 7.5.13, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
In various models of incompressible viscous fluids one of the most challenging problem is the construction of a pressure function, which can be regarded as a Lagrangian multiplier of the system due to the restrain of divergence free condition of the velocity of the fluid. While for the well-known Navier-Stokes equations this problem can be solved by using the L^p theory for the Stokes operator for general fluid models the problem is unsolved. However, by introducing a new method of constructing a local pressure we are able to prove the existence of a weak solution to such systems, satisfying a new form of local energy identity involving the local pressure. This eventually\nwill lead new results of partial regularity of weak solutions to the equations of Non-Newtonian fluids.\n\n
Cusped Shell-like Structures
Dienstag, 7.5.13, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
The talk is devoted to an updated exploratory survey of results concerning elastic\ncusped shells, plates, and beams and cusped prismatic shell-fluid interaction\nproblems. Mathematically, the corresponding problems lead to non-\nclassical, in general, boundary value and initial-boundary value problems for\ngoverning degenerate elliptic and hyperbolic systems in static and dynamical\ncases, respectively, with the corresponding mechanical (physical) interpretations.\nTwo principally different approaches of investigation are used:\n(1) to get results for 2D (two-dimensional) and 1D (one-dimensional) problems\nfrom results of the corresponding 3D (three-dimensional) problems and (2) to\ninvestigate directly governing degenerate and singular systems of 2D and 1D\nproblems. In both the cases, it is important to study the relationship of 2D and 1D\nproblems with 3D problems. On the one hand, it turned out that the second\napproach allows to investigate such 2D and 1D problems whose corresponding 3D\nproblems are not possible to study within the framework of the 3D model of the\ntheory of elasticity. On the other hand, the second approach is historically\napproved, since first the 1D and 2D models were created and only then the 3D\nmodel was constructed. Hence, the second approach gives a good chance for the\nfurther development (generalization) of the 3D model.
On the existence of a local pressure for general systems of incompressible viscous fluids
Dienstag, 7.5.13, 15:15-16:15, Raum 226, Hermann-Herder-Str. 10
In various models of incompressible viscous fluids one of the most challenging problem is the construction of a pressure function, which can be regarded as a Lagrangian multiplier of the system due to the restrain of divergence free condition of the velocity of the fluid. While for the well-known Navier-Stokes equations this problem can be solved by using the \(L^p\) theory for the Stokes operator for general fluid models the problem is unsolved. However, by introducing a new method of constructing a local pressure we are able to prove the existence of a weak solution to such systems, satisfying a new form of local energy identity involving the local pressure. This eventually will lead new results of partial regularity of weak solutions to the equations of Non-Newtonian fluids.
Basic findings to Stokes eigenfunctions and notes on applications in rotating Hagen-Poiseuille flow in pipes
Dienstag, 14.5.13, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
We give an overview on results, techniques, decomposition methods and constraints for the determination of eigenfunctions of the Stokes operator with homogeneous Dirichlet boundary conditions on the rigid part of the frontier of three-dimensional domains.\nWe explain wherefore the class of three-dimensional domains accessible for the specification of Stokes eigenfunctions is resticted on only five elements, namely at first the ball and the annulus - and secondary the infinite layer, the interior of a pipe and the interior of a double pipe \n(all equipped with periodic conditions).\nFurthermore, we illustrate the particular importance of explicitely known Stokes eigenfunctions emphasized by the fact, that one needs a good deal more information then - only the existence and completeness of such systems - in calculations and estimations. There we present the numerical\nstudy of rotating Hagen-Poiseuille flow as an example of applications also.