Sufficient conditions on Liouville type theorems for the 3D steady Navier--Stokes equations
Algebra i analiz, Tome 31 (2019) no. 2, pp. 269-278.

Voir la notice de l'article provenant de la source Math-Net.Ru

Our aim is to prove Liouville type theorems for the three dimensional steady-state Navier–Stokes equations provided the velocity field belongs to some Lorentz spaces. The corresponding statement contains several known results as a particular case.
Keywords: Liouville theorem, Navier–Stokes equations, Lorentz spaces.
@article{AA_2019_31_2_a11,
     author = {G. Seregin and W. Wang},
     title = {Sufficient conditions on {Liouville} type theorems for the {3D} steady {Navier--Stokes} equations},
     journal = {Algebra i analiz},
     pages = {269--278},
     publisher = {mathdoc},
     volume = {31},
     number = {2},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2019_31_2_a11/}
}
TY  - JOUR
AU  - G. Seregin
AU  - W. Wang
TI  - Sufficient conditions on Liouville type theorems for the 3D steady Navier--Stokes equations
JO  - Algebra i analiz
PY  - 2019
SP  - 269
EP  - 278
VL  - 31
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AA_2019_31_2_a11/
LA  - en
ID  - AA_2019_31_2_a11
ER  - 
%0 Journal Article
%A G. Seregin
%A W. Wang
%T Sufficient conditions on Liouville type theorems for the 3D steady Navier--Stokes equations
%J Algebra i analiz
%D 2019
%P 269-278
%V 31
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AA_2019_31_2_a11/
%G en
%F AA_2019_31_2_a11
G. Seregin; W. Wang. Sufficient conditions on Liouville type theorems for the 3D steady Navier--Stokes equations. Algebra i analiz, Tome 31 (2019) no. 2, pp. 269-278. http://geodesic.mathdoc.fr/item/AA_2019_31_2_a11/

[1] Chae D., “Liouville-type theorem for the forced Euler equations and the Navier–Stokes equations”, Comm. Math. Phys., 326:1 (2014), 37–48 | DOI | MR | Zbl

[2] Chae D., Yoneda T., “On the Liouville theorem for the stationary Navier–Stokes equations in a critical space”, J. Math. Anal. Appl., 405:2 (2013), 706–710 | DOI | MR | Zbl

[3] Chae G., Wolf J., On Liouville type theorems for the steady Navier–Stokes equations in $R^3$, arXiv: 1604.07643 | MR

[4] Chae D., Weng S., “Liouville type theorems for the steady axially symmetric Navier–Stokes and magnetohydrodynamic equations”, Discrete Contin. Dyn. Syst., 36:10 (2016), 5267–5285 | DOI | MR | Zbl

[5] Galdi G. P., An introduction to the mathematical theory of the Navier–Stokes equations. Steady-state problems, Springer Monogr. Math., Second ed., Springer, New York, 2011 | DOI | MR | Zbl

[6] Koch G., Nadirashvili N., Seregin G., Sverak V., “Liouville theorems for the Navier–Stokes equations and applications”, Acta Math., 203:1 (2009), 83–105 | DOI | MR | Zbl

[7] Kozono H., Terasawa Y., Wakasugi Y., “A remark on Liouville-type theorems for the stationary Navier–Stokes equations in three space dimensions”, J. Funct. Anal., 272 (2017), 804–818 | DOI | MR | Zbl

[8] Seregin G., “Liouville type theorem for stationary Navier–Stokes equations”, Nonlinearity, 29:8 (2016), 2191–2195 | DOI | MR | Zbl

[9] Seregin G., A Liouville type theorem for steady-state Navier–Stokes equations, arXiv: ; J. E. D. P., IX, 2016, 5 pp. 1611.01563

[10] Seregin G., “Remarks on Liouville type theorems for steady-state Navier–Stokes equations”, Algebra i analiz, 30:2 (2018), 238–248, arXiv: 1703.10822v1 | MR