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Global solutions of the 2D Euler equations, starting with the work of Witold Wolibner

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Warianty tytułu
Konferencja
6th European Congress of Mathematics, 2-7 July 2012 Kraków
Języki publikacji
EN
Abstrakty
Słowa kluczowe
Rocznik
Strony
257--269
Opis fizyczny
Bibliogr. 28 poz.
Twórcy
  • Institut für Mathematik Universität Leipzig D-04103 Leipzig Johannisgasse 26 Germany
Bibliografia
  • [1] L. Ambrosio, Transport equation and Cauchy problem for BV vector fields, Invent. Math. 158 (2004), no. 2, 227-260.
  • [2] A. L. Bertozzi, P. Constantin, Global regularity for vortex patches, Commun. Math. Phys. 152 (1993), no. 1, 19-28.
  • [3] Y. Brenier, C. De Lellis, L. Székelyhidi, Weak-strong uniqueness for measure-valued solutions, Comm. Math. Phys. 305 (2011), no. 2, 351-361.
  • [4] J.-Y. Chemin, Sur le mouvement des particules d’un fluids parfait incompressible bidimensionnel, Invent. Math. 103 (1991), no. 3, 599-629.
  • [5] J.-Y. Chemin, Perfect incompressible fluids, Clarendon Press, Oxford 1998. Transl. from the French by Isabelle Gallagher and Dragos Iftimie.
  • [6] J.-M. Delort, Existence of vortex sheets in dimension two (Existence de nappes de tourbillon en dimension deux), J. Amer. Math. Soc. 4 (1991), no. 3, 553-586.
  • [7] R. J. DiPerna, P.L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989), no. 3, 511-547.
  • [8] C. De Lellis, ODEs with Sobolev coefficients: the Eulerian and the Lagrangian approach, Discrete Contin. Dyn. Syst. Ser. S 1 (2008), no. 3, 405-426,
  • [9] C. De Lellis, L. Székelyhidi., The Euler equations as a differential inclusion, Ann. of Math. 170 (2009), no. 3, 1417-1436.
  • [10] C. De Lellis, L. Székelyhidi., On admissibility criteria for weak solutions of the Euler equations, Arch. Ration. Mech. Anal. 195 (2010), no, 1, 225-260.
  • [11] C. De Lellis, L. Székelyhidi., The h-principle and the equations of fluid dynamics (2011), preprint.
  • [12] C. De Lellis, L. Szekelyhidi Jr., Dissipative continuous Euler flows (2012), preprint.
  • [13] R. J. DiPerna, A. Majda, Concentrations in regularizations for 2-D incompressible flow, Comm. Pure Appl. Math. 40 (1987), no. 3, 301-345.
  • [14] L. C. Evans, S. Müller, Hardy spaces and the two-dimensional Euler equations with nonnegative vorticity, J. Amer. Math. Soc. 7 (1994), no. 1,199-219.
  • [15] N. M. Günther, Uber ein Hauptproblem der Hydrodynamik, Math. Z. 24 (1925), 448-499.
  • [16] E. Hölder, Über die unbeschränkte Fortsetzbarkeiteiner stetigen ebenen Bewegung in einer unbegrenzten inkompressiblen Flüssigkeit, Math. Z. 37 (1933), 727-738.
  • [17] E. Kamke, Über die eindeutige Bestimmtheit der Morale von Differentiateichungen, Math. Z. 32 (1930), 101-107.
  • [18] L. Lichtenstein, Über einige Existenzprobleme der Hydrodynamik homogener, unzusammendrückbarer, reibungsloser Flüssigkeiten und die Helmholtzschen Wirbelsätze, Math. Z. 23 (1925), 89-154.
  • [19] L. Lichtenstein, Grundlagen der Hydromechanik 1929.
  • [20] P. L. Lions, Mathematical topics in fluid mechanics, vol. 1, Incompressible models, Oxford Lecture Series in Mathematics and its Applications, vol. 3, Oxford Science Publications, The Clarendon Press Oxford University Press, New York 1996.
  • [21] A. Majda, Vorticity and the mathematical theory of incompressible fluid flow, Comm. Pure Appl. Math. 39 (1986), no. S, S187-S220.
  • [22] A. Majda, A. Bertozzi, Vorticity and incompressible flow, Cambridge Texts in Applied Mathematics, vol. 27, Cambridge University Press, Cambridge 2002.
  • [23] C. W. Oseen, Neuere Methoden und Ergebnisse in der Hydrodynamik 1927.
  • [24] V. Scheffer, An inviscid flow with compact support in space-time, J. Geom. Anal. 3 (1993). no. 4, 343-401.
  • [25] A. Shnirelman, On the nonuniqueness of weak solution of the Euler equation, Comm. Pure Appl. Math. 50 (1997), no. 12, 1261-1286.
  • [26] L. Székelyhidi Jr., Weak solutions to the incompressible Euler equations with vortex sheet initial data, C. R., Math., Acad. Sci. Paris 349 (2011), no. 19-20, 1063-1066.
  • [27] W. Wolibner, Un théorème sur l’existence du mouvement plan d’unfluide parfait, homogene, incompressible, pendant un temps infiniment long, Math. Z. 37 (1933). 698-726
  • [28] V. I. Yudovich, Non-stationary flows of an ideal incompressible fluid, Ż. Vycisl. Mat. i Mat. Rz. 3 (1963), 1032-1066.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-255a37a6-26de-46f6-8447-97d00265ecaa
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