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Journées équations aux dérivées partielles

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Gregory Seregin
A Liouville type theorem for steady-state Navier-Stokes equations
Journées équations aux dérivées partielles (2016), Exp. No. 9, 5 p., doi: 10.5802/jedp.650
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Résumé - Abstract

A Liouville type theorem is proven for the steady-state Navier-Stokes equations. It follows from the corresponding theorem on the Stokes equations with the drift. The drift is supposed to belong to a certain Morrey space.


[1] Chae, D., Liouville-Type Theorem for the Forced Euler Equations and the Navier-Stokes Equations, Comm. Math. Phys. 326 (2014): 37-48.  MR 3162482
[2] Chae, D., Yoneda, T., On the Liouville theorem for the stationary Navier-Stokes equations in a critical space, J. Math. Anal. Appl. 405 (2013), no. 2: 706-710.
[3] Chae, G., Wolf, J., On Liouville type theorems for the steady Navier-Stokes equations in $R^3$, arXiv:1604.07643.
[4] Galdi, G. P., An introduction to the mathematical theory of the Navier-Stokes equations. Steady-state problems. Second edition. Springer Monographs in Mathematics. Springer, New York, 2011.
[5] Giaquinta, M., Multiple integrals in the calculus of variations and nonlinear elliptic systems. Annals of Mathematics Studies, 105. Princeton University Press, Princeton, NJ, 1983.
[6] 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 (1978), no. 2: 381-404.
[7] Koch, G., Nadirashvili, N., Seregin, G., Sverak, V., Liouville theorems for the Navier-Stokes equations and applications, Acta Math. 203 (2009): 83–105.
[8] Nazarov, A. I. and Uraltseva, N. N., The Harnack inequality and related properties for solutions to elliptic and parabolic equations with divergence-free lower-order coefficients, St. Petersburg Mathematical Journal 23 (1): 93–115, 2012.
[9] Seregin, G., Liouville type theorem for stationary Navier-Stokes equations, Nonlinearity, 29 (2016): 2191–2195.
[10] Stein, E. M. Singular integrals and differentiability properties of functions. Princeton Mathematical Series, No. 30 Princeton University Press, Princeton, N.J. 1970.  MR 290095
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