Existence of weak solutions for unsteady motions of generalized Newtonian fluids
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 9 (2010) no. 1, pp. 1-46.

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.

Classification: 76D03, 35D05, 35D46, 34A34
Diening, Lars 1; Růžička, Michael 1; Wolf, Jörg 2

1 Universität Freiburg, Mathematisches Institut, Eckerstr, 1, 79104 Freiburg, Germany
2 Otto-von-Guericke-Universität Magdeburg, Universitätsplatz 2, Postfach 4120, 39106 Magdeburg, Germany
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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, Serie 5, Volume 9 (2010) no. 1, pp. 1-46. http://archive.numdam.org/item/ASNSP_2010_5_9_1_1_0/

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