We prove the existence of weak solutions of the equations of unsteady motion of an incompressible fluid with shear-dependent viscosity in a cylinder , where denotes a bounded domain. Under the assumption that the extra stress tensor possesses a -structure with , we are able to construct a weak solution with . Our approach is based on the Lipschitz truncation method, which is new in this context.
@article{ASNSP_2010_5_9_1_1_0, author = {Diening, Lars and R\r{u}\v{z}i\v{c}ka, Michael and Wolf, J\"org}, title = {Existence of weak solutions for unsteady motions of generalized {Newtonian} fluids}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, pages = {1--46}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 9}, number = {1}, year = {2010}, mrnumber = {2668872}, zbl = {1253.76017}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2010_5_9_1_1_0/} }
TY - JOUR AU - Diening, Lars AU - Růžička, Michael AU - Wolf, Jörg TI - Existence of weak solutions for unsteady motions of generalized Newtonian fluids JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2010 SP - 1 EP - 46 VL - 9 IS - 1 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2010_5_9_1_1_0/ LA - en ID - ASNSP_2010_5_9_1_1_0 ER -
%0 Journal Article %A Diening, Lars %A Růžička, Michael %A Wolf, Jörg %T Existence of weak solutions for unsteady motions of generalized Newtonian fluids %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2010 %P 1-46 %V 9 %N 1 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2010_5_9_1_1_0/ %G en %F ASNSP_2010_5_9_1_1_0
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, pp. 1-46. http://www.numdam.org/item/ASNSP_2010_5_9_1_1_0/
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