A remark on the uniqueness problem for the weak solutions of Navier-Stokes equations

Francis Ribaud

Annales de la Faculté des sciences de Toulouse : Mathématiques (2002)

  • Volume: 11, Issue: 2, page 225-238
  • ISSN: 0240-2963

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Ribaud, Francis. "A remark on the uniqueness problem for the weak solutions of Navier-Stokes equations." Annales de la Faculté des sciences de Toulouse : Mathématiques 11.2 (2002): 225-238. <http://eudml.org/doc/73579>.

@article{Ribaud2002,
author = {Ribaud, Francis},
journal = {Annales de la Faculté des sciences de Toulouse : Mathématiques},
keywords = {uniqueness; weak solutions; Navier-Stokes equations},
language = {eng},
number = {2},
pages = {225-238},
publisher = {UNIVERSITE PAUL SABATIER},
title = {A remark on the uniqueness problem for the weak solutions of Navier-Stokes equations},
url = {http://eudml.org/doc/73579},
volume = {11},
year = {2002},
}

TY - JOUR
AU - Ribaud, Francis
TI - A remark on the uniqueness problem for the weak solutions of Navier-Stokes equations
JO - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY - 2002
PB - UNIVERSITE PAUL SABATIER
VL - 11
IS - 2
SP - 225
EP - 238
LA - eng
KW - uniqueness; weak solutions; Navier-Stokes equations
UR - http://eudml.org/doc/73579
ER -

References

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  1. [A] Adams ( R.). - Sobolev Spaces, Pure and applied math. series, V. 65, Academic Press, 1978. Zbl0314.46030MR450957
  2. [FJR] Fabes ( E.B.), Jones ( B.F.) and Riviere ( N.). - The initial boundary value problem for the Navier-Stokes equation with initial data in Lp, Arch. Rat. Mech. Anal., V. 45 (1972), p. 222-240. Zbl0254.35097MR316915
  3. [FLR] Furioli ( G.), Lemarié-Rieusset ( P.-G.) and Terraneo ( E.). - Unicité dans L3(R3) et d'autres espaces fonctionnels limites pour Navier-Stokes, Rev. Mat. Iberoamericana, V. 16(3) (2000), p. 605-667. Zbl0970.35101MR1813331
  4. [G] Giga ( Y.). - Solutions for Semilinear Equations in Lp and Regularity of Weak Solutions of the Navier-stokes System, J. Diff. Equa., V. 62 (1986), p. 186-212. Zbl0577.35058MR833416
  5. [GP] Gallagher ( I.) and Planchon ( F.). - On infinite energy solutions to the Navier-Stokes equations: global 2D existence and 3D weak-strong uniqueness, to appear in Arch. Rational. Mech. Anal. MR1891170
  6. [L] Leray ( J.). - Sur le mouvement d'un liquide visqueux emplissant l'espace, Acta. Math., V. 63 (1934), p. 193-248. JFM60.0726.05
  7. [Li] Lions ( J.L.). - Quelques méthodes de résolutions des problèmes aux limites non-linéaires, Dunod, Paris, 1969. Zbl0189.40603MR259693
  8. [LM] Lions ( P.-L.), Masmoudi ( N.). - Uniqueness of mild solutions of the Navier-Stokes system in LN, Comm. Partial Differential Equations, 26(11-12) (2001), p. 2211-2226. Zbl1086.35077MR1876415
  9. [P] Prodi ( G.). - Un teorama di unicita per le equazioni di Navier-Stokes, Annali di Mat., V. 48 (1959), p. 173-182. Zbl0148.08202MR126088
  10. [RS] Runst ( T.) and Sickel ( W.). - Sobolev spaces of fractional order, Nemytskij operators and nonlinear partial differential equations, de Gruyter, Berlin, 1996. Zbl0873.35001MR1419319
  11. [S] Serrin ( J.). — The initial value problem for the Navier-Stokes equations, Non-linear Problems (R. Langer ed.), p. 69-98, Madison : The University of Wisconsin press, 1963. Zbl0115.08502MR150444
  12. [SW] Sohr ( H.) and Von Wahl ( W.). - On the singular set and the uniqueness of weak solutions of the Navier-Stokes equations, man. math., V. 49 (1984), p. 27-59. Zbl0567.35069MR762786
  13. [T] Temam ( R.). - Navier-stokes Equations,, North-Holland, Amsterdam, 1984. Zbl0568.35002MR769654
  14. [Tr] Triebel ( H.). - Theory of function spaces II, Birkhauser, 1992. MR1163193

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