Existence of solution for the Euler equations in a critical Besov space B∞,11(ℝn)

Communications in Partial Differential Equations

Volumn 29, Issue 7-8, 2004, Pages 1149-1166

  Pak, Hee Chul ^a   Park, Young Ja ^b  

^a Dankook University   (South Korea)

^b Sejong University   (South Korea)

Author keywords

Besov spaces; Euler equations; Existence of solution; Ideal incompressible fluids

Indexed keywords

EID: 8744277357     PISSN: 03605302     EISSN: None     Source Type: Journal    
DOI: 10.1081/PDE-200033764     Document Type: Article

References (15)

1. Bahouri, H., Chemin, J.-Y. (1994). Equations de transport relatives à des champs des vecteurs non-lipschitziens et mécanique des fluides. Arch. Rational Mech. Anal. 127:159-199.
2. Bahouri, H., Dehman, B. (1994). Remarques sur l'apparition de singularités dans les écoulements Eulériens incompressibles à donnée initiale Höldérienne. J. Math. Pures Appl. 73:335-346.
3. Beale, J. T., Kato, T., Majda, A. (1984). Remarks on the breakdown of smooth solutions for the 3-D Euler equations. Comm. Math. Phys. 94:61-66.
4. Bony, J. M. (1981). Calcul symbolique et propagation des singularitiés pour les équations aux dérivées partielles non linéaires. Ann. de l'Ecole Norm. Sup. 14:209-246.
5. Chae, D. (2002). On the well-posedness of the Euler equations in the Triebel-Lizorkin spaces. Comm. Pure Appl. Math. 55(5):654-678.
6. Chae, D. (2004). Local existence and blow-up criterion for the Euler equations in the Besov spaces. Asymptotic Analysis 38:339-358.
7. Chemin, J.-Y. (1998). Perfect Incompressible Fluids. Oxford: Clarendon Press.
8. Ponce, G. (1985). Remarks on a paper by J. T. Beale, T. Kato and A. Majda. Comm. Math. Phys. 98:349-353.
9. s type. Z. Anal. Anwendungen 14:105-140.
10. Stein, E. M. (1993). Harmonic Analysis; Real-Variable Methods, Orthogonality, and Osillatory Integrals. Princeton Mathematical Series 43, Monographs in Harmonic Analysis, III. Princeton, NJ: Princeton University.
11. Taylor, M. E. (2000). Tools for PDE Pseudodifferential Operators, Paradifferential Operators, and Layer Potentials. Mathematical surveys and Monographs, Vol. 81. AMS.
12. Triebel, H. (1983). Theory of Function Spaces. Birkhäuser.
13. Vishik, M. (1998). Hydrodynamics in Besov spaces. Arch. Rational Mech. Anal. 145:197-214.
14. e série, t. 32:769-812.
15. Vishik, M. (2000). Incompressible flows of an ideal fluid with unbounded vorticity. Comm. Math. Phys. 213:697-731.