Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 32 (1999) no. 6, pp. 769-812. 
@article{ASENS_1999_4_32_6_769_0,
     author = {Vishik, Misha},
     title = {Incompressible flows of an ideal fluid with vorticity in borderline spaces of {Besov} type},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {769--812},
     publisher = {Elsevier},
     volume = {Ser. 4, 32},
     number = {6},
     year = {1999},
     doi = {10.1016/s0012-9593(00)87718-6},
     mrnumber = {2000i:76008},
     zbl = {0938.35128},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1016/s0012-9593(00)87718-6/}
}
TY  - JOUR
AU  - Vishik, Misha
TI  - Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type
JO  - Annales scientifiques de l'École Normale Supérieure
PY  - 1999
SP  - 769
EP  - 812
VL  - 32
IS  - 6
PB  - Elsevier
UR  - http://archive.numdam.org/articles/10.1016/s0012-9593(00)87718-6/
DO  - 10.1016/s0012-9593(00)87718-6
LA  - en
ID  - ASENS_1999_4_32_6_769_0
ER  - 
%0 Journal Article
%A Vishik, Misha
%T Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type
%J Annales scientifiques de l'École Normale Supérieure
%D 1999
%P 769-812
%V 32
%N 6
%I Elsevier
%U http://archive.numdam.org/articles/10.1016/s0012-9593(00)87718-6/
%R 10.1016/s0012-9593(00)87718-6
%G en
%F ASENS_1999_4_32_6_769_0
Vishik, Misha. Incompressible flows of an ideal fluid with vorticity in borderline spaces of Besov type. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 32 (1999) no. 6, pp. 769-812. doi : 10.1016/s0012-9593(00)87718-6. http://archive.numdam.org/articles/10.1016/s0012-9593(00)87718-6/

[BC] H. Bahouri and J.-Y. Chemin, Equations de transport relatives à des champs de vecteurs on-lipschitziens et mécanique des fluides, Arch. Rational Mech. Anal., Vol. 127, 1994, pp. 159-181. | MR | Zbl

[BKM] T. Beale, T. Kato and A. Majda, Remarks on the breakdown of smooth for the 3-D Euler equations, Comm. Math. Phys., Vol. 94, 1984, pp. 61-66. | MR | Zbl

[B] J.-M. Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. de l'Ecole Norm. Sup., Vol. 14, 1981, pp. 209-246. | EuDML | Numdam | MR | Zbl

[BB] J. Bourguignon and H. Brezis, Remarks on the Euler equation, J. Funct. Anal., Vol. 15, 1974, no. 4, pp. 341-363. | MR | Zbl

[C] D. Chae, Weak solutions of 2D Euler equations with initial vorticity in L log L(R2), J. Diff. Equat., Vol. 103, 1993, pp. 323-337. | MR | Zbl

[C1] J.-Y. Chemin, Fluides parfaits incompressibles, Astérisque no. 230, 1995. | Numdam | MR | Zbl

[C2] J.-Y. Chemin, Persistance de structures géométriques dans les fluides incompressibles bidimensionnelles, Ann. Ecole Norm. Sup., Vol. 26, 1993, pp. 1-26. | EuDML | Numdam | MR | Zbl

[CL] J.-Y. Chemin and N. Lerner, Flot de champs de vecteurs non Lipschitziens et équations de Navier-Stokes, J. Diff. Equat., Vol. 121, 1995, pp. 314-328. | MR | Zbl

[D] I. Daubechies, Ten lectures on wavelets, SIAM, 1992. | MR | Zbl

[De] J.-M. Delort, Existence de nappes de tourbillon en dimension deux, J. Amer. Math. Soc., Vol. 4, 1991, pp. 553-586. | MR | Zbl

[D1] B. Desjardins, A few remarks on ordinary differential equations, Commun. in PDE's, Vol. 21, 1966, pp. 1667-1703. | MR | Zbl

[D2] B. Desjardins, Linear transport equations with initial values in Sobolev spaces and application to Navier-Stokes equations, Diff. And Int. Equat., Vol. 10, 1997, no. 3, pp. 577-586. | MR | Zbl

[DL] R. Di Perna and P.-L. Lions, Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math., Vol. 98, 1989, no. 3, pp. 511-549. | MR | Zbl

[DM] R. Di Perna and A. Majda, Concentrations in regularizations for 2-D incompressible flows, Comm. Pure Appl. Math., Vol. 40, 1987, pp. 301-345. | MR | Zbl

[EM] D. Ebin and J. Marsden, Groups of diffeomorphismes and the motion of an incompressible fluid, Ann. of Math., Vol. 92, 1970, pp. 102-163. | MR | Zbl

[EVM] L.C. Evans and S. Múller, Hardy spaces and the two-dimensional Euler equations with non-negative vorticity, J. Amer. Math. Soc., Vol. 7, 1994, pp. 199-220. | MR | Zbl

[FJ] M. Frazier and B. Jawerth, Decomposition of Besov spaces, Indiana Math. J., Vol. 34, 1985, pp. 777-799. | MR | Zbl

[Ge] P. Gérard, Résultats récents sur les fluides parfaits incompressibles bidimensionnels [d'après J.-Y. Chemin et J.-M. Delort], Seminar Bourbaki, 1991/1992, no. 757, Astérisque, Vol. 206, 1992, pp. 411-444. | Numdam | Zbl

[G] N. Gunther, On the motion of fluid in a moving container, Izvestia Akad. Nauk USSR, Ser. Fiz.-Math., Vol. 20, 1927, pp. 1323-1348, 1503-1532 ; Vol. 21, 1927, pp. 521-526, 735-756 ; Vol. 22, 1928, pp. 9-30.

[KP] T. Kato and G. Ponce, Well posedness of the Euler and Navier-Stokes equations in Lebesgue spaces Lsp(R2), Revista Ibero-Americana, Vol. 2, 1986, pp. 73-88. | MR | Zbl

[LM] P. Lemarié and Y. Meyer, Ondelettes et bases hilbertiennes, Revista Ibero-Americana, Vol. 2, 1986, pp. 1-18. | MR | Zbl

[L] L. Lichtenstein, Über einige Existenzprobleme der Hydrodynamik homogenerun-zusammendrück barer, reibungsloser Flüβigkeiten und die Helmgoltzschen Wirbelsatze0, Math. Z., Vol. 23, 1925, pp. 89-154 ; Vol. 26, 1927, pp. 196-323 ; Vol. 28, 1928, pp. 387-415 ; Vol. 32, 1930, pp. 608-725. | JFM

[M] A. Majda, Remarks on weak solutions for vortex sheets with a distinguished sign, Indiana Univ. Math. J., Vol. 42, 1993, pp. 921-939. | MR | Zbl

[M1] Y. Meyer, Remarques sur un théorème de J.-M. Bony, Suppl. Rend. Circ. Mat. Palermo, Vol. 1, 1981, pp. 1-20. | MR | Zbl

[M2] Y. Meyer, Wavelets and operators, Cambridge University Press, 1992. | MR | Zbl

[P] J. Peetre, New Thoughts on Besov Spaces, Duke Univ. Press, 1976. | MR | Zbl

[S] V. Scheffer, An inviscid flow with compact support in space-time, J. of Geom. Anal., Vol. 3, 1993, no. 4, pp. 343-401. | MR | Zbl

[Sh] A. Shnirelman, On the non-uniqueness of weak solution of the Euler equations, Comm. Pure Appl. Math., Vol. 50, 1997, no. 12, pp. 1261-1286. | MR | Zbl

[T] R. Temam, Local existence of C∞ solutions of the Euler equations of incompressible perfect fluid, Lecture Notes in Math., Vol. 565, 1976, pp. 184-194. | MR | Zbl

[Tr] H. Triebel, Theory of Function Spaces 2, Birkhauser, 1992. | MR

[Y1] V. Yudovich, Nonstationary flow of an ideal incompressible liquid, Zh. Vych. Mat., Vol. 3, 1963, pp. 1032-1066. | Zbl

[Y2] V. Yudovich, Uniqueness theorem for the basic nonstationary problem in the dynamics of an ideal incompressible fluid, Mathematical Research Letters, Vol. 2, 1995, pp. 27-38. | MR | Zbl

[Y3] V. Yudovich, Some bounds of solutions of elliptic equations, Mat. Sbornik, Vol. 59, 1962, pp. 229-244. | MR | Zbl

[V] M. Vishik, Hydrodynamics in Besov spaces, Arch. for Rat. Mech. and Anal., Vol. 145, 1998, pp. 197-214. | MR | Zbl

[W] W. Wolibner, Un théorème sur l'existence du mouvement plan d'un fluide parfait, homogène, incompressible, pendant un temps infiniment long, Math. Z., Vol. 37, 1933, pp. 698-627. | JFM | Zbl

Cité par Sources :