This chapter primarily deals with internal, isothermal, unsteady flows of a class of
incompressible fluids with both constant and shear or pressure dependent viscosity that …

Certain rheological behavior of non-Newtonian fluids in engineering sciences is often
modeled by a power law ansatz with p∈(1, 2]. In the present paper the local in time …

Local-in-time well-posedness of the initial-boundary value problem for a class of non-
Newtonian Navier–Stokes problems on domains with compact C^3--boundary is proven in …

We prove Hölder continuity of gradient of a unique weak solution for unsteady generalized
Navier–Stokes equations with p (x, t)-power law with Dirichlet type boundary condition under …

Long-time and large-data existence of weak solutions for initial-and boundary-value
problems concerning three-dimensional flows of incompressible fluids is nowadays …

We study interior regularity of solutions of a generalized stationary Stokes problem in the
plane. The main, elliptic part of the problem is given in the form div (A (D u)) div (A (D u)) …

We consider an optimal control problem for the evolutionary flow of incompressible non-
Newtonian fluids in a two-dimensional domain. The existence of optimal controls is proven …

In some recent papers we have been pursuing regularity results up to the boundary, in W2, l
(Ω) spaces for the velocity, and in W1, l (Ω) spaces for the pressure, for fluid flows with shear …

We study a planar flow of a generalized Newtonian fluid under the Dirichlet boundary
condition. The fluid is characterized by a nonlinear dependence of the stress tensor on the …

We prove regularity estimates for time derivatives of a large class of nonlinear parabolic
partial differential systems. This includes the instationary (symmetric) p-Laplace system and …