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Original Articles

Conservation of Geometric Structures for Non-Homogeneous Inviscid Incompressible Fluids

Pages 1553-1595 | Received 22 Sep 2011, Accepted 24 Apr 2012, Published online: 21 Aug 2012

References

  • Alinhac , S. ( 1988 ). Interaction d'ondes simples pour des equations complètement non linéaires. [Simple wave interaction for completely nonlinear systems] . Ann. Sci. École Norm. Sup. 21 : 91 – 133 .
  • Bahouri , H. , Chemin , J.-Y. , Danchin , R. ( 2011 ). Fourier Analysis and Nonlinear Partial Differential Equations . Grundlehren der Mathematischen Wissenschaften (Fundamental Principles of Mathematical Sciences) , Vol. 343 . Heidelberg : Springer .
  • Bony , J.-M. ( 1980 ). Propagation des singularités pour des equations aux dérivées partielles non linéaires [Propagation of singularities for nonlinear partial differential equations]. Séminaires Équations aux Dérivées Partielles de l’École Polytechnique. Paris: I’École Polytechnique .
  • Bony , J.-M. ( 1981 ). Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires [Symbolic calculus and propagation of singularities for nonlinear partial differential equations] . Ann. Sci. École Norm. Sup. 14 : 209 – 246 .
  • Chemin , J.-Y. (1988). Calcul paradifférentiel précisé et application à des équations aux dérivées partielles non linéaire [“Specified” paradifferencial calculus and applications to nonsemilinear partial differential equations]. Duke Math. J. 51(1):431–469.
  • Chemin , J.-Y. ( 1991 ). Sur le mouvement des particules d'un fluide parfait, incompressible, bidimensionel . Inventiones Mathematicae 103 : 599 – 629 .
  • Chemin , J.-Y. ( 1993 ). Persistance des structures géométriques liées aux poches de tourbillon [Persistence of geometric stuctures associated with vortex patches] . Ann. Sci. École Norm. Sup. 26 ( 4 ): 1 – 26 .
  • Chemin , J.-Y. ( 1995 ). Fluides parfaits incompressibles [Incompressible perfect fluids]. Astérisque 230 . Paris : Société Mathématique de France .
  • Danchin , R. ( 1997 ). Poches de tourbillon visqueuses [Viscous vortex patches] . J. Math. Pures Appl. 76 : 609 – 647 .
  • Danchin , R. ( 1997 ). Évolution temporelle d'une poche de tourbillon singulière [Temporal evalution of a singular vortex patch] . Comm. Part. Diff. Eqs. 22 : 685 – 721 .
  • Danchin , R. ( 1999 ). Persistance de structures géométriques et limite non visqueuse pour les fluides incompressibles en dimension quelconque [Persistance of geometric structures and inviscid limit for incompressible fluids in any dimension] . Bull. Soc. Math. France 127 ( 2 ): 179 – 227 .
  • Danchin , R. ( 2010 ). On the well-posedness of the incompressible density-dependent Euler equations in the L p framework . J. Diff. Eqs. 248 ( 8 ): 2130 – 2170 .
  • Danchin , R. , Fanelli , F. ( 2011 ). The well-posedness issue for the density-dependent Euler equations in endpoint Besov spaces . J. Math. Pure Appl. 96 ( 3 ): 253 – 278 .
  • Dautray , R. , Lions , J.-L. ( 1990 ). Mathematical Analysis and Numerical Methods for Sciences and Technology , Vol. 1 . Berlin : Springer-Verlag .
  • Depauw , N. ( 1999 ). Poche de tourbillon pour Euler 2D dans un ouvert à bord [Vortex patch for 2D Euler in an open board] . J. Math. Pures Appl. 78 : 313 – 351 .
  • Dutrifoy , A. ( 2003 ). On 3-D vortex patches in bounded domains . Comm. Part. Diff. Eqs. 28 ( 7–8 ): 1237 – 1263 .
  • Gamblin , P. , Saint-Raymond , X. ( 1995 ). On three-dimensional vortex patches . Bull. Soc. Math. France 123 : 375 – 424 .
  • Gilbarg , D. , Trudinger , N. S. ( 1985 ). Elliptic Partial Differential Equations of Second Order . New York : Springer-Verlag .
  • Hatcher , A. ( 2002 ). Algebraic Topology . Cambridge : Cambridge University Press .
  • Hmidi , T. ( 2005 ). Régularité höldérienne des poches de tourbillon visqueuses [Hölder regularity of viscous vortex patches] . J. Math. Pure Appl. 84 ( 11 ): 1455 – 1495 .
  • Huang , C. ( 2001 ). Singular integral system approach to regularity of 3D vortex patches . Indiana Univ. Mathe. J. 50 ( 1 ): 509 – 552 .
  • Lima , E.L. ( 1988 ). The Jordan-Brouwer separation theorem for smooth hypersurfaces . Amer. Math. Monthly 95 ( 1 ): 39 – 42 .
  • Majda , A. ( 1986 ). Vorticity and the mathematical theory of an incompressible fluid flow . Comm. Pure Appl. Math. 38 : 187 – 220 .
  • Serfati , P. ( 1994 ). Régularité stratifiée et équation d'Euler 3D à temps grand [Stratified regularity and 3D Euler equations] . C. R. Acad. Sci. Paris Sér I Math. 318 : 925 – 928 .
  • Yudovich , V. ( 1963 ). Non stationary flow of an ideal incompressible fluid . Zh. Vychisl. Mat. i Mat. Fiz. 3 : 1032 – 1066 .

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