On Pressure Boundary Conditions for Steady Flows of Incompressible Fluids with Pressure and Shear Rate Dependent Viscosities

Authors: Martin Lanzendörfer, Jan Stebel
Publication year: 2011
Publication type: Článek v odborném periodiku
Periodical: Applications of Mathematics
Bibliographic citation: LANZENDÖRFER, Martin, STEBEL, Jan. On Pressure Boundary Conditions for Steady Flows of Incompressible Fluids with Pressure and Shear Rate Dependent Viscosities. Applications of Mathematics. 2011, 56(3), 265-285. ISSN 0862-7940. E-ISSN 1572-9109
Dostupné z: doi:10.1007/s10492-011-0016-1.
DOI: 10.1007/s10492-011-0016-1
ID: 331366

Abstract

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 in- flow/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.