caa a22 4500 463170903 CHVBK 20180406164812.0 cr unu---uuuuu 170326e20070301xx s 000 0 eng 10.1007/s00021-006-0219-5 doi (NATIONALLICENCE)springer-10.1007/s00021-006-0219-5 Wolf Jörg Humboldt-Universität zu Berlin, Unter den Linden. 6, 10099, Berlin, BRD aut Existence of Weak Solutions to the Equations of Non-Stationary Motion of Non-Newtonian Fluids with Shear Rate Dependent Viscosity [Elektronische Daten] [Jörg Wolf] Abstract.: In the present paper we prove the existence of weak solutions $$ u:Q \to \mathbb{R}^{n}$$ to the equations of non-stationary motion of an incompressible fluid with shear rate dependent viscosity in a cylinder Q = Ω × (0,T), where $$ \Omega \subset \mathbb{R}^{n} $$ denotes an open set. For the power-low model with $$ q > 2\frac{{n + 1}}{{n + 2}}$$ we are able to construct a weak solution $$ u\in L^q(0, T; W_0^{1,q}(\Omega)^n)\cap C_w([0,T];L^2(\Omega)^n)$$ with ∇ · u = 0. Birkhäuser Verlag, Basel, 2006 Non-Newtonian fluids nationallicence Dirichlet boundary initial value problem nationallicence weak solutions nationallicence local pressure method nationallicence Journal of Mathematical Fluid Mechanics Birkhäuser-Verlag; www.birkhäuser.ch 9/1(2007-03-01), 104-138 1422-6928 9:1<104 2007 9 21 https://doi.org/10.1007/s00021-006-0219-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00021-006-0219-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Wolf Jörg Humboldt-Universität zu Berlin, Unter den Linden. 6, 10099, Berlin, BRD aut NATIONALLICENCE 773 0- Journal of Mathematical Fluid Mechanics Birkhäuser-Verlag; www.birkhäuser.ch 9/1(2007-03-01), 104-138 1422-6928 9:1<104 2007 9 21 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer