Diening, Lars; Růžička, Michael; Wolf, Jörg
Existence of weak solutions for unsteady motions of generalized Newtonian fluids
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5 : Tome 9 (2010) no. 1 , p. 1-46
Zbl 1253.76017 | MR 2668872
URL stable : http://www.numdam.org/item?id=ASNSP_2010_5_9_1_1_0

Classification:  76D03,  35D05,  35D46,  34A34
We prove the existence of weak solutions 𝐮:Q T n of the equations of unsteady motion of an incompressible fluid with shear-dependent viscosity in a cylinder Q T =Ω×(0,T), where Ω n denotes a bounded domain. Under the assumption that the extra stress tensor 𝐒 possesses a q-structure with q>2n n+2, we are able to construct a weak solution 𝐮L q (0,T;W 0 1,q (Ω))C w ([0,T];L 2 (Ω)) with div𝐮=0. Our approach is based on the Lipschitz truncation method, which is new in this context.

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