We consider stationary Navier–Stokes equations in with a regular external force and we prove the exponential frequency decay of the solutions. Moreover, if the external force is small enough, we give a pointwise exponential frequency decay for such solutions. If a damping term is added to the equation, a pointwise decay is obtained without the smallness condition over the force.
Pour une force extérieure quelconque, mais suffisamment régulière, on démontre la décroissance fréquentielle des solutions de ces équations. Si, de plus, la force est petite, on peut décrire ponctuellement cette décroissance. La condition de petitesse de la force peut être supprimée si l'on rajoute un terme d'amortissement.
Accepted:
Published online:
Diego Chamorro 1; Oscar Jarrín 1; Pierre-Gilles Lemarié-Rieusset 1
@article{CRMATH_2019__357_2_175_0, author = {Diego Chamorro and Oscar Jarr{\'\i}n and Pierre-Gilles Lemari\'e-Rieusset}, title = {Frequency decay for {Navier{\textendash}Stokes} stationary solutions}, journal = {Comptes Rendus. Math\'ematique}, pages = {175--179}, publisher = {Elsevier}, volume = {357}, number = {2}, year = {2019}, doi = {10.1016/j.crma.2018.12.007}, language = {en}, }
TY - JOUR AU - Diego Chamorro AU - Oscar Jarrín AU - Pierre-Gilles Lemarié-Rieusset TI - Frequency decay for Navier–Stokes stationary solutions JO - Comptes Rendus. Mathématique PY - 2019 SP - 175 EP - 179 VL - 357 IS - 2 PB - Elsevier DO - 10.1016/j.crma.2018.12.007 LA - en ID - CRMATH_2019__357_2_175_0 ER -
Diego Chamorro; Oscar Jarrín; Pierre-Gilles Lemarié-Rieusset. Frequency decay for Navier–Stokes stationary solutions. Comptes Rendus. Mathématique, Volume 357 (2019) no. 2, pp. 175-179. doi : 10.1016/j.crma.2018.12.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2018.12.007/
[1] Gevrey class regularity for the solutions of the Navier–Stokes equations, J. Funct. Anal., Volume 87 (1989), pp. 359-369
[2] Gevrey regularity for the attractor of the 3D Navier–Stokes–Voight equations, J. Nonlinear Sci., Volume 19 (2009), pp. 133-149
[3] The Mathematical Theory of Viscous Incompressible Flow, Gordon and Breach, New York–London, 1963
[4] Une remarque sur l'analycité des solutions mild des équations de Navier–Stokes dans , C. R. Acad. Sci. Paris, Ser. I, Volume 330 (2000) no. 3, pp. 183-186
[5] The Navier–Stokes Problem in the 21st Century, Chapman & Hall/CRC, 2016
[6] A note on Gevrey class regularity for the solutions of the Navier–Stokes equations, J. Math. Anal. Appl., Volume 167 (1992), pp. 588-595
Cited by Sources:
Comments - Policy