The chemotaxis–Navier–Stokes system
The present work gives an affirmative answer to the question of global solvability for (⋆) in the following sense: Under mild assumptions on the initial data, and under modest structural assumptions on f and χ, inter alia allowing for the prototypical case when
This solution is obtained as the limit of smooth solutions to suitably regularized problems, where appropriate compactness properties are derived on the basis of a priori estimates gained from an energy-type inequality for (⋆) which in an apparently novel manner combines the standard dissipation property of the fluid evolution with a quasi-dissipative structure associated with the chemotaxis subsystem in (⋆).
Keywords: Chemotaxis, Navier–Stokes, Global existence
@article{AIHPC_2016__33_5_1329_0, author = {Winkler, Michael}, title = {Global weak solutions in a three-dimensional {chemotaxis{\textendash}Navier{\textendash}Stokes} system}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {1329--1352}, publisher = {Elsevier}, volume = {33}, number = {5}, year = {2016}, doi = {10.1016/j.anihpc.2015.05.002}, zbl = {1351.35239}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.002/} }
TY - JOUR AU - Winkler, Michael TI - Global weak solutions in a three-dimensional chemotaxis–Navier–Stokes system JO - Annales de l'I.H.P. Analyse non linéaire PY - 2016 SP - 1329 EP - 1352 VL - 33 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.002/ DO - 10.1016/j.anihpc.2015.05.002 LA - en ID - AIHPC_2016__33_5_1329_0 ER -
%0 Journal Article %A Winkler, Michael %T Global weak solutions in a three-dimensional chemotaxis–Navier–Stokes system %J Annales de l'I.H.P. Analyse non linéaire %D 2016 %P 1329-1352 %V 33 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.002/ %R 10.1016/j.anihpc.2015.05.002 %G en %F AIHPC_2016__33_5_1329_0
Winkler, Michael. Global weak solutions in a three-dimensional chemotaxis–Navier–Stokes system. Annales de l'I.H.P. Analyse non linéaire, Volume 33 (2016) no. 5, pp. 1329-1352. doi : 10.1016/j.anihpc.2015.05.002. http://www.numdam.org/articles/10.1016/j.anihpc.2015.05.002/
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