Free Access
Volume 47, Number 3, May-June 2013
Page(s) 663 - 688
Published online 04 March 2013
  1. G.A. Baker and P. Graves-Morris, Padé approximants, 2nd edition, Cambridge University Press, Cambridge. Encycl. Math. Appl. 59 (1996). [Google Scholar]
  2. M.S. Baouendi and C. Goulaouic, Sharp estimates for analytic pseudodifferential operators and application to Cauchy problems. J. Differ. Equ. 48 (1983) 241–268. [CrossRef] [Google Scholar]
  3. C. Bardos and S. Benachour, Domaine d’analycité des solutions de l’équation d’Euler dans un ouvert de Rn. Annal. Scuola Norm. Sup. Pisa Cl. Sci. 4 (1977) 647–687. [Google Scholar]
  4. C. Bardos and E.S. Titi, Euler equations for incompressible ideal fluids. Russian Math. Surveys 62 (2007) 409–451. [CrossRef] [MathSciNet] [Google Scholar]
  5. J. T. Beale, T. Kato and A. Majda, Remarks on the breakdown of smooth solutions for the 3D Euler equations. Commun. Math. Phys. 94 (1984) 61–66. [CrossRef] [MathSciNet] [Google Scholar]
  6. E. Behr, J. Nečas and H. Wu, On blow-up of solution for Euler equations. ESAIM: M2AN 35 (2001) 229–238. [CrossRef] [EDP Sciences] [Google Scholar]
  7. N. Bourbaki, Éléments de Mathématique. Variétés différentielles et analytiques, Fascicule de résultats, Hermann, Paris (1971). [Google Scholar]
  8. M.E. Brachet, D. Meiron, S. Orszag, B. Nickel, R. Morf and U. Frisch, Small scale structure of the Taylor–Green vortex. J. Fluid Mech. 130 (1983) 411–452. [NASA ADS] [CrossRef] [Google Scholar]
  9. M.E. Brachet, D. Meiron, S. Orszag, B. Nickel, R. Morf and U. Frisch, The Taylor–Green vortex and fully developed turbulence. J. Statist. Phys. 34 (1984) 1049-1063. [CrossRef] [MathSciNet] [Google Scholar]
  10. M.E. Brachet, M. Meneguzzi, A. Vincent, H. Politano and P.L. Sulem, Numerical evidence of smooth self-similar dynamics and possibility of subsequent collapse for three-dimensional ideal flows. Phys. Fluids A 4 (1992) 2845–2854. [CrossRef] [Google Scholar]
  11. T. Chen and N. Pavlović, A lower bound on blowup rates for the 3D incompressible Euler equation and a single exponential Beale–Kato–Majda estimate completer. ArXiv:1107.0435v1 [math.AP] (2011). [Google Scholar]
  12. S.I. Chernyshenko, P. Constantin, J.C. Robinson and E.S. Titi, A posteriori regularity of the three-dimensional NavierStokes equations from numerical computations. J. Math. Phys. 48 (2007) 065–204. [CrossRef] [Google Scholar]
  13. U. Frisch, Fully developed turbulence and singularities, in Chaotic Behavior of Deterministic Systems, edited by G. Iooss, R.H.G. Helleman, R. Stora. LesHouches, session XXXVI, North-Holland, Amsterdam (1983) 665–704. [Google Scholar]
  14. U. Frisch, T. Matsumoto and J. Bec, Singularities of the Euler flow? Not out of the blue!. J. Stat. Phys. 113 (2003) 761–781. [CrossRef] [Google Scholar]
  15. T. Kato, Quasi-linear equations of evolution, with applications to partial differential equations, in Spectral theory and differential equations, Proceedings of the Dundee Symposium. Lect. Notes Math. 448 (1975) 23-70. [Google Scholar]
  16. S. Kida, Three-dimensional periodic flows with high-symmetry. J. Phys. Soc. Japan 54 (1985) 2132–2140. [CrossRef] [Google Scholar]
  17. R.H. Morf, S.A. Orszag and U. Frisch, Spontaneous singularity in three-dimensional inviscid, incompressible flow. Phys. Rev. Lett. 44 (1980) 572-574. [CrossRef] [Google Scholar]
  18. M. Morimoto, Analytic functionals on the sphere. AMS, Providence. Transl. Math. Monogr. 178 (1998). [Google Scholar]
  19. C. Morosi and L. Pizzocchero, On approximate solutions of semilinear evolution equations II. Generalizations, and applications to Navier–Stokes equations. Rev. Math. Phys. 20 (2008) 625–706. [CrossRef] [MathSciNet] [Google Scholar]
  20. C. Morosi, L. Pizzocchero, An H1 setting for the Navier–Stokes equations: Quantitative estimates. Nonlinear Anal. 74 (2011) 2398–2414. [CrossRef] [MathSciNet] [Google Scholar]
  21. C. Morosi and L. Pizzocchero, On approximate solutions of the incompressible Euler and Navier–Stokes equations. Nonlinear Anal. 75 (2012) 2209–2235. [CrossRef] [MathSciNet] [Google Scholar]
  22. R.B. Pelz, Extended series analysis of full octahedral flow: numerical evidence for hydrodynamic blowup. Fluid Dyn. Res. 33 (2003) 207–221. [CrossRef] [Google Scholar]
  23. H. Stahl, The convergence of diagonal Padé approximants and the Padé conjecture. J. Comput. Appl. Math. 86 (1997) 287–296. [CrossRef] [Google Scholar]
  24. S.P. Suetin, Padé approximants and efficient analytic continuation of a power series. Russian Math. Surveys 57 (2002) 43–141. [CrossRef] [MathSciNet] [Google Scholar]
  25. F. Treves, Topological vector spaces, distributions and kernels. Academic Press, New York (1967). [Google Scholar]
  26. GMPY Collaboration, Multiprecision arithmetic for Python, This software is a wrapper for GMP Multiple Precision Arithmetic Library, see [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you