On inhomogeneous incompressible fluids and reverse Hölder inequalities

Arina Arkhipova; Olga Ladyzhenskaya

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)

  • Volume: 25, Issue: 1-2, page 51-67
  • ISSN: 0391-173X

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Arkhipova, Arina, and Ladyzhenskaya, Olga. "On inhomogeneous incompressible fluids and reverse Hölder inequalities." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 25.1-2 (1997): 51-67. <http://eudml.org/doc/84295>.

@article{Arkhipova1997,
author = {Arkhipova, Arina, Ladyzhenskaya, Olga},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {summability with power; unique sovability; viscous incompressible inhomogeneous fluids; initial-boundary value problem; periodic boundary conditions; reverse Hölder inequalities},
language = {eng},
number = {1-2},
pages = {51-67},
publisher = {Scuola normale superiore},
title = {On inhomogeneous incompressible fluids and reverse Hölder inequalities},
url = {http://eudml.org/doc/84295},
volume = {25},
year = {1997},
}

TY - JOUR
AU - Arkhipova, Arina
AU - Ladyzhenskaya, Olga
TI - On inhomogeneous incompressible fluids and reverse Hölder inequalities
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1997
PB - Scuola normale superiore
VL - 25
IS - 1-2
SP - 51
EP - 67
LA - eng
KW - summability with power; unique sovability; viscous incompressible inhomogeneous fluids; initial-boundary value problem; periodic boundary conditions; reverse Hölder inequalities
UR - http://eudml.org/doc/84295
ER -

References

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  1. [1] O.A. Ladyzhenskaya - V.A. Solonnikov, On unique solvability of initial-boundary value problem for viscous incompressible nonhomogeneous fluids, Zapiski Nauchn. Semin. LOMI52 (1975), 52-109. Zbl0376.76021MR425391
  2. [2] A.A. Kiselev - O.A. Ladyzhenskaya, On existence and uniqueness of the solution of the nonstationary problemfor a viscous incompressible fluids, Izv. Akad. Nauk USSR, Ser. Mat.21 (1957), 655-680. Zbl0131.41201MR100448
  3. [3] O.A. Ladyzhenskaya, Solution "in the large" of the boundary value problem for the Navier-Stokes equations for the case of two space variables, Dokl. Akad. Nauk USSR123 (1958), 427-433. Zbl0090.41502
  4. [4] O.A. Ladyzhenskaya, "Mathematical Problems of the Dynamics for Viscous Incompressible Fluids", Moscow, 1961 (the first Russian edition); Moscow1970 (the second Russian edition). English translation of the first Russian Edition: "The Mathematical Theory of Viscous Incompressible Flow", Gordon and Breach, 1963. 
  5. [5] V.A. Solonnikov, On differential properties for the nonstationary Navier-Stokes equations, Trudy MIAN USSR73 (1964), 221-291. Zbl0163.33901MR172014
  6. [6] O.A. Ladyzhenskaya - V.A. Solonnikov - N.N. Uraltseva, "Linear and Quasilinear Equations of the Parabolic Type", Moscow, Nauka, 1967. Zbl0164.12302
  7. [7] O.A. Ladyzhenskaya - N.N. Uraltseva, "Linear and Quasilinear Equations of the Elliptic Type", Moscow, 1973 (the second Russian edition). Zbl0269.35029MR509265
  8. [8] F.W. Gehring, Lp-integrability of the partial derivatives of a quasi-conformal mapping, Acta Math.130 (1973), 265-277. Zbl0258.30021MR402038
  9. [9] M. Giaquinta - G. Modica, Regularity results for some classes of higher order nonlinear elliptic systems, J. Reine Angew. Math.311/312 (1979), 145-169. Zbl0409.35015MR549962
  10. [10] E.W. Stredulinsky, Higher integrability from reverse Hölder inequalities, Indiana Univ. Math. J.29 (1980), 408-417. Zbl0442.35064MR570689
  11. [11] M. Giaquinta - M. Struwe, On the partial regularity of weak solutions of nonlinear parabolic systems, Math. Z.179 (1982), 437-451. Zbl0469.35028MR652852
  12. [12] A. Arkhipova, Reverse Hölder inequalities with boundary integrals and Lp-estimates for solutions of nonlinear elliptic and parabolic boundary-value problems, Amer. Math. Soc. Transl.164 (1995), 15-42. Zbl0838.35021MR1334137

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