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On pressure boundary conditions for steady flows of incompressible fluids with pressure and shear rate dependent viscosities

Martin Lanzendörfer, Jan Stebel (2011)

Applications of Mathematics

We consider a class of incompressible fluids whose viscosities depend on the pressure and the shear rate. Suitable boundary conditions on the traction at the inflow/outflow part of boundary are given. As an advantage of this, the mean value of the pressure over the domain is no more a free parameter which would have to be prescribed otherwise. We prove the existence and uniqueness of weak solutions (the latter for small data) and discuss particular applications of the results.

On ∂̅-problems on (pseudo)-convex domains

R. Range (1995)

Banach Center Publications

In this survey we shall tour the area of multidimensional complex analysis which centers around ∂̅-problems (i.e., the Cauchy-Riemann equations) on pseudoconvex domains. Along the way we shall highlight some of the classical milestones as well as more recent landmarks, and we shall discuss some of the major open problems and conjectures. For the sake of simplicity we will only consider domains in n ; intriguing phenomena occur already in the simple setting of (Euclidean) convex domains. We will not...

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