Regularity in Sobolev Spaces of Steady Flows of Fluids with Shear-Dependent Viscosity
نویسنده
چکیده
The system −divS(D(u)) + (u · ∇)u +∇π = f , divu = 0, is considered on a bounded three-dimensional domain under no–stick boundary value conditions, where S has p-structure for some p < 2 and D(u) is the symmetrized gradient of u. Various regularity results for the velocity u and the pressure π in fractional order Sobolev and Nikolskii spaces are obtained.
منابع مشابه
A Composite Finite Difference Scheme for Subsonic Transonic Flows (RESEARCH NOTE).
This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...
متن کاملTime-periodic Electroosmotic Flow of Non-newtonian Fluids in Microchannels
The alternating current electroosmotic flow of a non-Newtonian power-law fluid is studied in a circular microchannel. A numerical method is employed to solve the non-linear Poisson-Boltzmann and the momentum equations. The main parameters which affect the flow field are the flow behavior index, the dimensionless zeta potential and the dimensionless frequency. At very low dimensionless frequenci...
متن کاملA nonsmooth model for discontinuous shear thickening fluids: Analysis and numerical solution
We propose a nonsmooth continuum mechanical model for discontinuous shear thickening flow. The model obeys a formulation as energy minimization problem and its solution satisfies a Stokes type system with a nonsmooth constitute relation. Solutions have a free boundary at which the behavior of the fluid changes. We present Sobolev as well as Hölder regularity results and study the limit of the m...
متن کاملOn steady flows of an incompressible fluids with implicit power-law-like rheology∗
We consider steady flows of incompressible fluids with power-law-like rheology given by an implicit constitutive equation relating the Cauchy stress and the symmetric part of the velocity gradient in such a way that it leads to a maximal monotone (possibly multivalued) graph. Such a framework includes Bingham fluids, Herschel-Bulkley fluids, and shear-rate dependent fluids with discontinuous vi...
متن کاملThe inviscid limit for density-dependent incompressible fluids
— This paper is devoted to the study of smooth flows of density-dependent fluids in RN or in the torus TN . We aim at extending several classical results for the standard Euler or Navier-Stokes equations, to this new framework. Existence and uniqueness is stated on a time interval independent of the viscosity μ when μ goes to 0. A blow-up criterion involving the norm of vorticity in L1(0, T ;L∞...
متن کامل