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Szósty problem milenijny : istnienie i regularność rozwiązań układu Naviera-Stokesa

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PL
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Rocznik
Tom
Strony
121--130
Opis fizyczny
Bibliogr. 30 poz.
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autor
  • Wrocław
Bibliografia
  • [1] L. Caffarelli, R. Kohn, L. Nirenberg, Partial regularity of suitable weak solutions of the Navier-Stokes equations, Comm. Pure Appl. Math. 35 (1982), 771-837.
  • [2] M. Cannone, Ondelettes, paraproduits et Navier-Stokes, Diderot Editeur, Paris, 1995.
  • [3] M. Cannone, A generalisation of a theorem by Kato on Navier-Stokes equations, Rev. Mat. Iberoamericana 13 (1997), 515-541.
  • [4] M. Cannone, Nombres de Reynolds, stabilité et Navier-Stokes, w: Evolution Equations: Existence and Singularities, Banach Center Publ. 52, Inst. Math. Polish Acad. Sci., Warszawa, 2000, 29-59.
  • [5] M. Cannone, Y. Meyer, Littlewood-Paley decomposition and the Navier-Stokes equations, Meth. Appl. Anal. 2 (1995), 307-319.
  • [6] M. Cannone, F. Planchоn, Self-similar solutions of the Navier-Stokes equations in Rn, Comm. Partial Differential Equations 21 (1996), 179-193.
  • [7] P. Constantin, A few results and open problems regarding incompressible fluids, Notices Amer. Math. Soc. 42, no. 6, 658-663.
  • [8] P. Constantin, C. Foiaş, Navier-Stokes Equations, Chicago Lectures in Math., Univ. of Chicago Press, Chicago, 1988.
  • [9] C. Foiaş,What do the Namer-Stokes equations tell us about turbulence?, w: Contemp. Math. 208, Amer. Math. Soc., 1997, 151-180.
  • [10] H. Fujita, T. Kato, On the Navier-Stokes initial value problem I, Arch. Rational Mech. Anal. 16 (1964), 269-315.
  • [11] G. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations, 2 tomy, Springer, New York, 1994.
  • [12] J. G. Heywood, Remarks on the possible global regularity of solutions of the three-dimensional Navier-Stokes equations, w: Progress in Theoretical and Computational Fluid Mechanics (Paseky, 1993), Pitman Res. Notes Math. Ser. 308, 1994, 1-32.
  • [13] E. Hоpf, Über die Anfangswertaufgabe für die hydrodynamischen Grundgleichungen, Math. Nachr. 4 (1951), 213-231.
  • [14] G. Karch, Scaling in nonlinear parabolic equations, J. Math. Anal. Appl. 234 (1999), 534-558.
  • [15] T. Kato, Strong Lp solutions of the Navier-Stokes equations in Rm with applications to weak solutions, Math. Z. 187 (1984), 471-480.
  • [16] T. Kato, H. Fujita, On the non-stationary Navier-Stokes system, Rend. Sem. Mat. Univ. Padova 32 (1962), 243-260.
  • [17] O. A. Ladyzhenskaya, The Mathematical Theory of Viscous Incompressible Flow, II wydanie, Gordon and Breach, New York, 1969.
  • [18] L. D. Landau, E. M. Lifschitz, Hydrodynamika, PWN, Warszawa, 1994.
  • [19] P.-G. Lemarié-Rieusset, Recent Developments in the Navier-Stokes Problem, Chapman & Hall, CRC Press, 2002.
  • [20] J. Leray, Sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Math. 63 (1934), 193-248.
  • [21] F.-H. Lin, A new proof of the Caffarelli-Kohn-Nirenberg theorem, Comm. Pure Appl. Math. 51 (1998), 240-257.
  • [22] J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969.
  • [23] P.-L. Lions, Mathematical Topics in Fluid Mechanics, The Clarendon Press, Oxford Univ. Press, New York, tom I, 1996, tom II, 1998.
  • [24] Y. Meyer, Wavelets, paraproducts and Navier-Stokes equations, w: Current Developments in Mathematics 1996, International Press, Cambridge, MA, 1999, 105-212.
  • [25] J. Nečas, M. Roužička, V. Šverák, On Leray self-similar solutions of the Navier-Stokes equations, Acta Math. 176 (1996), no. 2, 283-294.
  • [26] J. Serrin, The initial value problem for the Navier-Stokes equations, w: Nonlinear Problems, R. E. Langer (red.), Univ. of Wisconsin Press, Madison, WI, 1963, 69-98.
  • [27] R. Temam, Navier-Stokes Equations, North-Holland, Amsterdam, 1979.
  • [28] R. Temam, Some developments on Navier-Stokes equations in the second half of the 20th century, w: Development of Mathematics 1950-2000, J.-P. Pier (red.), 2000.
  • [29] W. von Wahl, The Equations of Navier-Stokes and Abstract Parabolic Equations, Aspekte der Mathematik, Vieweg & Sohn, Braunschweig/Wiesbaden, 1985.
  • [30] M. Wiegner, The Navier-Stokes equations — a neverending challenge?, Jahresber. Deutsch. Math.-Verein 101 (1999), 1-25.
Typ dokumentu
Bibliografia
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