In this paper, we address the problem of determining the asymptotic behaviour of the solutions of the incompressible stationary Navier–Stokes system in the full space, with a forcing term whose asymptotic behaviour at infinity is homogeneous of degree −3. We identify the asymptotic behaviour at infinity of the solution. We prove that it is homogeneous and that the leading term in the expansion at infinity uniquely solves the homogeneous Navier–Stokes equations with a forcing term which involves an additional Dirac mass. This also applies to the case of an exterior domain.
@article{AIHPC_2017__34_2_277_0, author = {Decaster, Agathe and Iftimie, Drago\c{s}}, title = {On the asymptotic behaviour of solutions of the stationary {Navier{\textendash}Stokes} equations in dimension 3}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {277--291}, publisher = {Elsevier}, volume = {34}, number = {2}, year = {2017}, doi = {10.1016/j.anihpc.2015.12.002}, mrnumber = {3610933}, zbl = {1373.35216}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2015.12.002/} }
TY - JOUR AU - Decaster, Agathe AU - Iftimie, Dragoş TI - On the asymptotic behaviour of solutions of the stationary Navier–Stokes equations in dimension 3 JO - Annales de l'I.H.P. Analyse non linéaire PY - 2017 SP - 277 EP - 291 VL - 34 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2015.12.002/ DO - 10.1016/j.anihpc.2015.12.002 LA - en ID - AIHPC_2017__34_2_277_0 ER -
%0 Journal Article %A Decaster, Agathe %A Iftimie, Dragoş %T On the asymptotic behaviour of solutions of the stationary Navier–Stokes equations in dimension 3 %J Annales de l'I.H.P. Analyse non linéaire %D 2017 %P 277-291 %V 34 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2015.12.002/ %R 10.1016/j.anihpc.2015.12.002 %G en %F AIHPC_2017__34_2_277_0
Decaster, Agathe; Iftimie, Dragoş. On the asymptotic behaviour of solutions of the stationary Navier–Stokes equations in dimension 3. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 2, pp. 277-291. doi : 10.1016/j.anihpc.2015.12.002. http://www.numdam.org/articles/10.1016/j.anihpc.2015.12.002/
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