Uniqueness of Leray solutions of the 3D Navier-Stokes equations is a challenging open problem. In this article we will study this problem for the 3D stationary Navier-Stokes equations in the whole space . Under some additional hypotheses, stated in terms of Lebesgue and Morrey spaces, we will show that the trivial solution is the unique solution. This type of results are known as Liouville theorems.
@article{AIHPC_2021__38_3_689_0,
author = {Chamorro, Diego and Jarr{\'\i}n, Oscar and Lemari\'e-Rieusset, Pierre-Gilles},
title = {Some {Liouville} theorems for stationary {Navier-Stokes} equations in {Lebesgue} and {Morrey} spaces},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
pages = {689--710},
publisher = {Elsevier},
volume = {38},
number = {3},
year = {2021},
doi = {10.1016/j.anihpc.2020.08.006},
mrnumber = {4227049},
zbl = {1466.35282},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.anihpc.2020.08.006/}
}
TY - JOUR AU - Chamorro, Diego AU - Jarrín, Oscar AU - Lemarié-Rieusset, Pierre-Gilles TI - Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces JO - Annales de l'I.H.P. Analyse non linéaire PY - 2021 SP - 689 EP - 710 VL - 38 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2020.08.006/ DO - 10.1016/j.anihpc.2020.08.006 LA - en ID - AIHPC_2021__38_3_689_0 ER -
%0 Journal Article %A Chamorro, Diego %A Jarrín, Oscar %A Lemarié-Rieusset, Pierre-Gilles %T Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces %J Annales de l'I.H.P. Analyse non linéaire %D 2021 %P 689-710 %V 38 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2020.08.006/ %R 10.1016/j.anihpc.2020.08.006 %G en %F AIHPC_2021__38_3_689_0
Chamorro, Diego; Jarrín, Oscar; Lemarié-Rieusset, Pierre-Gilles. Some Liouville theorems for stationary Navier-Stokes equations in Lebesgue and Morrey spaces. Annales de l'I.H.P. Analyse non linéaire, mai – juin 2021, Tome 38 (2021) no. 3, pp. 689-710. doi : 10.1016/j.anihpc.2020.08.006. http://www.numdam.org/articles/10.1016/j.anihpc.2020.08.006/
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