Remarks about the inviscid limit of the Navier-stokes system

Communications in Mathematical Physics

Volumn 270, Issue 3, 2007, Pages 777-788

  Masmoudi, Nader ^a  

^a NEW YORK UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33846833851     PISSN: 00103616     EISSN: 14320916     Source Type: Journal    
DOI: 10.1007/s00220-006-0171-5     Document Type: Article

References (24)

1. Abidi, H., Danchin, R.: Optimal bounds for the inviscid limit of Navier-Stokes equations. Asymptot. Anal. 38(1), 35-46 (2004)
2. Beirão da Veiga, H.: On the singular limit for slightly compressible fluids. Calc. Var. Part. Differ. Eqs. 2(2), 205-218 (1994)
3. Beirão da Veiga, H.: Singular limits in compressible fluid dynamics. Arch. Rat. Mech. Anal. 128(4), 313-327 (1994)
4. Bertozzi, A.L., Constantin, P.: Global regularity for vortex patches. Commun. Math. Phys. 152(1), 19-28 (1993)
5. Bona, J.L., Smith, R.: The initial-value problem for the Korteweg-de Vries equation. Philos. Trans. Roy. Soc. London Ser. A 278(1287), 555-601 (1975)
6. Bony, J.-M.: Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. Sci. École Norm. Sup. (4) 14(2), 209-246 (1981)
7. Chemin, J.-Y.: Persistance de structures géométriques dans les fluides incompressibles bidimensionnels. Ann. Sci. École Norm. Sup. (4) 26(4), 517-542 (1993)
8. Chemin, J.-Y.: Fluides parfaits incompressibles. Astérisque 230, 177 (1995)
9. Chemin, J.-Y.: A remark on the inviscid limit for two-dimensional incompressible fluids. Comm. Part. Differ. Eqs. 21(11-12), 1771-1779 (1996)
10. Constantin, P.: Note on loss of regularity for solutions of the 3-D incompressible Euler and related equations. Commun. Math. Phys. 104(2), 311-326 (1986)
11. Constantin, P., Wu, J.: Inviscid limit for vortex patches. Nonlinearity 8(5), 735-742 (1995)
12. Constantin, P., Wu, J.: The inviscid limit for non-smooth vorticity. Indiana Univ. Math. J. 45(1), 67-81 (1996)
13. Danchin, R.: Persistance de structures géométriques et limite non visqueuse pour les fluides incompressibles en dimension quelconque. Bull. Soc. Math. France 127(2), 179-227 (1999)
14. Dutrifoy, A.: On 3-D vortex patches in bounded domains. Comm. Part. Differ. Eqs. 28(7-8), 1237-1263 (2003)
15. Gamblin, P., Saint Raymond, X.: On three-dimensional vortex patches. Bull. Soc. Math. France 123(3), 375-424 (1995)
16. Huang, C.: Singular integral system approach to regularity of 3D vortex patches. Indiana Univ. Math. J. 50(1), 509-552 (2001)
17. 3. J. Funct. Anal. 9, 296-305 (1972)
18. Kato, T.: Quasi-linear equations of evolution, with applications to partial differential equations. In: Spectral Theory and Differential Equations (Proc. Sympos., Dundee, 1974; dedicated to Konrad Jörgens), Lecture Notes in Math., Vol. 448. Berlin: Springer, 1975, pp. 25-70
19. Majda, A.J., Bertozzi, A.L.: Vorticity and incompressible flow. Volume 27 of Cambridge Texts in Applied Mathematics. Cambridge: Cambridge University Press, 2002
20. Masmoudi, N. : The Euler limit of the Navier-Stokes equations, and rotating fluids with boundary. Arch. Rat. Mech. Anal. 142(4), 375-394 (1998)
21. Masmoudi, N.: Examples of singular limits in hydrodynamics. In: Handbook of Differential Equations, Vol. 3, pp. 195-275. North-Holland, Amsterdam (2007)
22. 3. Trans. Amer. Math. Soc. 157, 373-397 (1971)
23. Wolibner, W.: Un theorème sur l'existence du mouvement plan d'un fluide parfait, homogène, incompressible, pendant un temps infiniment long. Math. Z. 37(1), 698-726 (1933)
24. Yudovich, V.I.: Non-stationary flows of an ideal incompressible fluid, u Z. Vy Cisl. Mat. i Mat. Fiz. 3, 1032-1066 (1963)