[Solutions continues en la viscosité pour les équations d'Euler ou de Navier–Stokes avec des conditions aux limites de type Navier]
Pourvu que les données soient suffisamment régulières, il existe
Provided the initial velocity and the external body force are sufficiently smooth, there exist
Accepté le :
Publié le :
Hamid Bellout 1 ; Jiří Neustupa 2 ; Patrick Penel 3
@article{CRMATH_2009__347_19-20_1141_0, author = {Hamid Bellout and Ji\v{r}{\'\i} Neustupa and Patrick Penel}, title = {On viscosity-continuous solutions of the {Euler} and {Navier{\textendash}Stokes} equations with a {Navier-type} boundary condition}, journal = {Comptes Rendus. Math\'ematique}, pages = {1141--1146}, publisher = {Elsevier}, volume = {347}, number = {19-20}, year = {2009}, doi = {10.1016/j.crma.2009.09.007}, language = {en}, }
TY - JOUR AU - Hamid Bellout AU - Jiří Neustupa AU - Patrick Penel TI - On viscosity-continuous solutions of the Euler and Navier–Stokes equations with a Navier-type boundary condition JO - Comptes Rendus. Mathématique PY - 2009 SP - 1141 EP - 1146 VL - 347 IS - 19-20 PB - Elsevier DO - 10.1016/j.crma.2009.09.007 LA - en ID - CRMATH_2009__347_19-20_1141_0 ER -
%0 Journal Article %A Hamid Bellout %A Jiří Neustupa %A Patrick Penel %T On viscosity-continuous solutions of the Euler and Navier–Stokes equations with a Navier-type boundary condition %J Comptes Rendus. Mathématique %D 2009 %P 1141-1146 %V 347 %N 19-20 %I Elsevier %R 10.1016/j.crma.2009.09.007 %G en %F CRMATH_2009__347_19-20_1141_0
Hamid Bellout; Jiří Neustupa; Patrick Penel. On viscosity-continuous solutions of the Euler and Navier–Stokes equations with a Navier-type boundary condition. Comptes Rendus. Mathématique, Volume 347 (2009) no. 19-20, pp. 1141-1146. doi : 10.1016/j.crma.2009.09.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.09.007/
[1] Existence et unicité de la solution de l'équation d'Euler en dimension deux, J. Math. Anal. Appl., Volume 40 (1972), pp. 769-790
[2] H. Beirão da Veiga, F. Crispo, Sharp inviscid limit results under Navier type boundary condition. An
[3] A Navier–Stokes approximation of the 3D Euler equation with the zero flux on the boundary, J. Math. Fluid Mech., Volume 10 (2008), pp. 531-553
[4] On the Navier–Stokes equations with boundary conditions based on vorticity, Math. Nachr., Volume 269–270 (2004), pp. 59-72
[5] H. Bellout, J. Neustupa, P. Penel, On a ν-continuous family of strong solutions to the Euler or Navier–Stokes equations with the Navier-type boundary condition, preprint, 2009
[6] Remarks on the Euler equation, J. Funct. Anal., Volume 15 (1974), pp. 341-363
[7] The Navier–Stokes equations with the kinematic and vorticity boundary conditions on non-flat boundaries, December 2008 (preprint) | arXiv
[8] T. Kato, Remarks on zero viscosity limit for non-stationary Navier–Stokes flows with boundary, in: S.S. Chern (Ed.), Seminar on Nonlinear PDE, MSRI, 1984
[9] Non blow-up of the 3D Euler equations for a class of three dimensional initial data in cylindrical domains, Methods Appl. Anal., Volume 11 (2004) no. 4, pp. 605-634
[10] On the Euler equations of incompressible perfect fluids, J. Funct. Anal., Volume 20 (1975), pp. 32-43
[11] On the vanishing viscosity limit for the 3D Navier–Stokes equations with a slip boundary condition, Comm. Pure Appl. Math., Volume 60 (2007), pp. 1027-1055
- Fluid Equations, Equations of Motion for Incompressible Viscous Fluids (2021), p. 41 | DOI:10.1007/978-3-030-78659-5_2
- Validity of boundary layer theory for the 3D plane-parallel nonhomogeneous electrically conducting flows, Mathematical Methods in the Applied Sciences, Volume 44 (2021) no. 11, pp. 8862-8882 | DOI:10.1002/mma.7314 | Zbl:1469.76145
- Equatorial wave-current interactions, Waves in flows. Based on lectures given at the summer school, Prague, Czech Republic, August 27–31, 2018, Cham: Birkhäuser, 2021, pp. 49-92 | DOI:10.1007/978-3-030-67845-6_2 | Zbl:1479.76113
- The vanishing viscosity limit for some symmetric flows, Annales de l'Institut Henri Poincaré. Analyse Non Linéaire, Volume 36 (2019) no. 5, pp. 1237-1280 | DOI:10.1016/j.anihpc.2018.11.006 | Zbl:1416.35025
- Stokes and Navier-Stokes problems with Navier-type boundary condition in
-spaces, Differential Equations and Applications, Volume 11 (2019) no. 2, pp. 203-226 | DOI:10.7153/dea-2019-11-08 | Zbl:1433.35216 - Some properties on the surfaces of vector fields and its application to the Stokes and Navier-Stokes problems with mixed boundary conditions, Nonlinear Analysis. Theory, Methods Applications. Series A: Theory and Methods, Volume 113 (2015), pp. 94-114 | DOI:10.1016/j.na.2014.09.017 | Zbl:1304.35551
- Inviscid limit for Navier-Stokes equations in domains with permeable boundaries, Applied Mathematics Letters, Volume 33 (2014), pp. 6-11 | DOI:10.1016/j.aml.2014.02.012 | Zbl:1314.76024
- On
-stability of strong solutions of the Navier-Stokes equations with the Navier-type boundary conditions, Journal of Mathematical Analysis and Applications, Volume 405 (2013) no. 2, pp. 731-737 | DOI:10.1016/j.jmaa.2013.04.037 | Zbl:1306.35086 - Boundary layer problem: Navier-Stokes equations and Euler equations, Nonlinear Analysis. Real World Applications, Volume 14 (2013) no. 6, pp. 2091-2104 | DOI:10.1016/j.nonrwa.2013.03.003 | Zbl:1302.76060
- Boundary layer analysis of the Navier-Stokes equations with generalized Navier boundary conditions, Journal of Differential Equations, Volume 253 (2012) no. 6, pp. 1862-1892 | DOI:10.1016/j.jde.2012.06.008 | Zbl:1248.35144
- On viscosity-continuous solutions of the Euler and Navier-Stokes equations with a Navier-type boundary condition, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 347 (2009) no. 19-20, pp. 1141-1146 | DOI:10.1016/j.crma.2009.09.007 | Zbl:1180.35405
Cité par 11 documents. Sources : Crossref, zbMATH
Commentaires - Politique
Vous devez vous connecter pour continuer.
S'authentifier