On the Euler Equations in the Critical Triebel-Lizorkin Spaces

Archive for Rational Mechanics and Analysis

Volumn 170, Issue 3, 2003, Pages 185-210

  Chae, Dongho ^a  

^a Seoul National University   (South Korea)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0344551939     PISSN: 00039527     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00205-003-0271-8     Document Type: Article

References (32)

1. BAHOURI, H., CHEMIN, J.Y.: Equations de transport relatives à des champs des vecteurs non-lipshitziens et mé canique des fluides. Arch. Rational Mech. Anal. 127, 159-199 (1994)
2. BAHOURI, H., DEHMAN, B.: Remarques sur l'apparition de singularités dans les écoulements Eulériens incompressibles à donnée initiale Höldérienne. J. Math. Pures Appl. 73, 335-346 (1994)
3. BEALE, J.T., KATO, T., MAJDA, A.: Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Comm. Math. Phys. 94, 61-66 (1984)
4. BONY, J.M.: Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires. Ann. de l'Ecole Norm. Sup. 14, 209-246 (1981)
5. CANNONE, M.: Ondelettes, Paraproduits et Navier-Stokes. Diderot Editeur (1995)
6. CANNONE, M.: Nombres de Reynolds, stabilité et Navier-Stokes. Banach Center Publication, (1999)
7. CHAE, D.: On the Well-Posedness of the Euler Equations in the Besov and the Triebel-Lizorkin Spaces. Proceedings of the Conference, "Tosio Kato's Method and Principle for Evolution Equations in Mathematical Physics", June 27-29 (2001)
8. CHAE, D.: On the Well-Posedness of the Euler Equations in the Triebel-Lizorkin Spaces. Comm. Pure Appl. Math 55, 654-678 (2002)
9. CHEMIN, J.Y.: Perfect incompressible fluids. Clarendon Press, Oxford (1998)
10. CHEMIN, J.Y.: Régularité des trajectoires des particules d'un fluide incompressible remplissant l'espace. J. Math. Pures Appl. 71, 407-417 (1992)
11. FRAZIER, M., JAWERTH, B., WEISS, G.: Littlewood-Paley theory and the study of function spaces. AMS-CBMS Regional Conference Series in Mathematics, 79 (1991)
12. α,q. Revista Mathemática Ibero-Americana 4, 41-72 (1988]
13. JAWERTH, B.: Some observations on Besov and Lizorkin-Triebel Spaces. Math. Sacand. 40, 94-104 (1977)
14. 3. J. Functional Anal. 9, 296-305 (1972)
15. KATO, T.: untitled manuscript. Proceedings of the Conference, "Tosio Koto's Method and Principle for Evolution Equations in Mathematical Physics", June 27-29 (2001)
16. KATO, T., PONCE, G.: Commutator estimates and the Euler and Navier-Stokes equations. Comm. Pure Appl. Math. 41, 891-907 (1988)
17. 2). Duke Math. J. 55, 487-499 (1987)
18. 2). Revista Mathemática Ibero-Americana 2, 73-88 (1986)
19. KOZONO, H., TANIUCHI, Y.: Limiting case of the Sobolev inequality in BMO, with applications to the Euler equations. Comm. Math. Phys. 214, 191-200 (2000)
20. KOZONO, H., OGAWA, T., TANIUCHI, Y.: The Critical Sobolev Inequalities in Besov Spaces and Regularity Criterion to Some Semilinear Evolution Equations. Preprint (2001)
21. LICHTENSTEIN, L.: Über einige Existenzprobleme der Hydrodynamik homogener unzusammendrückbarer, reibunglosser Flüssikeiten und die Helmholtzschen Wirbelsalitze. Math. Zeit. 23, 89-154 (1925); 26, 193-323, 387-415 (1927); 32, 608-725 (1930)
22. LICHTENSTEIN, L.: Über einige Existenzprobleme der Hydrodynamik homogener unzusammendrückbarer, reibunglosser Flüssikeiten und die Helmholtzschen Wirbelsalitze. Math. Zeit. 23, 89-154 (1925); 26, 193-323, 387-415 (1927); 32, 608-725 (1930)
23. LICHTENSTEIN, L.: Über einige Existenzprobleme der Hydrodynamik homogener unzusammendrückbarer, reibunglosser Flüssikeiten und die Helmholtzschen Wirbelsalitze. Math. Zeit. 23, 89-154 (1925); 26, 193-323, 387-415 (1927); 32, 608-725 (1930)
24. MAJDA, A.: Vorticity and the mathematical theory of incompressible fluid flow. Comm. Pure Appl. Math. 39, 187-220 (1986)
25. MAJDA, A.: Mathematical theory of fluid mechanics. Princeton University Graduate Course Lecture Note (1986)
26. s type. Z. Anal. Anwendungen. 14, 105-140 (1995)
27. STEIN, E.M.: Harmonic analysis; Real-variable methods, orthogonality, and oscillatory integrals. Princeton Mathematical Series 43 1993
28. TRIEBEL, H.: Theory of Function Spaces. Birkhäuser, (1983)
29. TRIEBEL, H.: Theory of Function Spaces II. Birkhäuser, (1992)
30. YUDOVICH, V.: Nonstationary flow of an ideal incompressible liquid. Zh. Vych. Mat. 3, 1032-1066 (1963)
31. VISHIK, M.: Hydrodynamics in Besov spaces. Arch. Rational Mech. Anal. 145, 197-214 (1998)
32. VISHIK, M.: Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type. Ann. Sci. École Norm. Sup. (4) 32, 769-812 (1999)