Remarks on Liouville type theorems for steady-state Navier–Stokes equations
Algebra i analiz, Tome 30 (2018) no. 2, pp. 238-248 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Liouville type theorems for the stationary Navier–Stokes equations are proved under certain assumptions. These assumptions are motivated by conditions that appear in Liouville type theorems for the heat equations with a given divergence free drift.
Keywords: Navier–Stokes equations
Mots-clés : Liouville type theorem.
@article{AA_2018_30_2_a9,
     author = {G. Seregin},
     title = {Remarks on {Liouville} type theorems for steady-state {Navier{\textendash}Stokes} equations},
     journal = {Algebra i analiz},
     pages = {238--248},
     year = {2018},
     volume = {30},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AA_2018_30_2_a9/}
}
TY  - JOUR
AU  - G. Seregin
TI  - Remarks on Liouville type theorems for steady-state Navier–Stokes equations
JO  - Algebra i analiz
PY  - 2018
SP  - 238
EP  - 248
VL  - 30
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/AA_2018_30_2_a9/
LA  - en
ID  - AA_2018_30_2_a9
ER  - 
%0 Journal Article
%A G. Seregin
%T Remarks on Liouville type theorems for steady-state Navier–Stokes equations
%J Algebra i analiz
%D 2018
%P 238-248
%V 30
%N 2
%U http://geodesic.mathdoc.fr/item/AA_2018_30_2_a9/
%G en
%F AA_2018_30_2_a9
G. Seregin. Remarks on Liouville type theorems for steady-state Navier–Stokes equations. Algebra i analiz, Tome 30 (2018) no. 2, pp. 238-248. http://geodesic.mathdoc.fr/item/AA_2018_30_2_a9/

[1] Bourguignon J. P., Brezis H., “Remarks on the Euler equation”, J. Funct. Anal., 15 (1974), 341–363 | DOI | MR

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

[3] 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

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

[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

[6] Giaquinta M., Multiple integrals in the calculus of variations and nonlinear elliptic systems, Ann. of Math. Stud., 105, Princeton Univ. Press, Princeton, NJ, 1983 | MR

[7] Gilbarg D., Weinberger H. F., “Asymptotic properties of steady plane solutions of the Navier–Stokes equations with bounded Dirichlet integral”, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 5:2 (1978), 381–404 | MR

[8] 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

[9] Nazarov A. I., Uraltseva N. N., “Neravenstvo Garnaka i svyazannye s nim svoistva reshenii ellipticheskikh i parabolicheskikh uravnenii s bezdivergentnymi mladshimi koeffitsientami”, Algebra i analiz, 23:1 (2011), 136–168 | MR | Zbl

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

[11] Seregin G., A Liouville type theorem for steady-state Navier–Stokes equations, arXiv: 1611.01563

[12] Seregin G., Silvestre L., Sverak V., Zlatos A., “On divergence-free drifts”, J. Differential Equations, 252:1 (2012), 505–540 | DOI | MR

[13] Stein E. M., Singular integrals and differentiability properties of functions, Princeton Math. Ser., 30, Princeton Univ. Press, Princeton, N.J., 1970 | MR