On evolution inequalities of a modified Navier-Stokes type. I

Manfred Müller; Joachim Naumann

Aplikace matematiky (1978)

  • Volume: 23, Issue: 3, page 174-184
  • ISSN: 0862-7940

Abstract

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The paper present an existence theorem for a strong solution to an abstract evolution inequality where the properties of the operators involved are motivated by a type of modified Navier-Stokes equations under certain unilateral boundary conditions. The method of proof rests upon a Galerkin type argument combined with the regularization of the functional.

How to cite

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Müller, Manfred, and Naumann, Joachim. "On evolution inequalities of a modified Navier-Stokes type. I." Aplikace matematiky 23.3 (1978): 174-184. <http://eudml.org/doc/15048>.

@article{Müller1978,
abstract = {The paper present an existence theorem for a strong solution to an abstract evolution inequality where the properties of the operators involved are motivated by a type of modified Navier-Stokes equations under certain unilateral boundary conditions. The method of proof rests upon a Galerkin type argument combined with the regularization of the functional.},
author = {Müller, Manfred, Naumann, Joachim},
journal = {Aplikace matematiky},
keywords = {existence and regularity of solutions; boundary value problems; viscous incompressible fluid; modified Navier-Stokes equations; evolution inequalities; Faedo-Galerkin approximation; existence and regularity of solutions; boundary value problems; viscous incompressible fluid; modified Navier-Stokes equations; evolution inequalities; Faedo-Galerkin approximation},
language = {eng},
number = {3},
pages = {174-184},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On evolution inequalities of a modified Navier-Stokes type. I},
url = {http://eudml.org/doc/15048},
volume = {23},
year = {1978},
}

TY - JOUR
AU - Müller, Manfred
AU - Naumann, Joachim
TI - On evolution inequalities of a modified Navier-Stokes type. I
JO - Aplikace matematiky
PY - 1978
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 23
IS - 3
SP - 174
EP - 184
AB - The paper present an existence theorem for a strong solution to an abstract evolution inequality where the properties of the operators involved are motivated by a type of modified Navier-Stokes equations under certain unilateral boundary conditions. The method of proof rests upon a Galerkin type argument combined with the regularization of the functional.
LA - eng
KW - existence and regularity of solutions; boundary value problems; viscous incompressible fluid; modified Navier-Stokes equations; evolution inequalities; Faedo-Galerkin approximation; existence and regularity of solutions; boundary value problems; viscous incompressible fluid; modified Navier-Stokes equations; evolution inequalities; Faedo-Galerkin approximation
UR - http://eudml.org/doc/15048
ER -

References

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  1. Biroli M., Sur l'inéquation d'évolution de Navier-Stokes, Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat., (8) 52 (1972); Nota I: 457-459; Nota II: 591-598; Nota III: 811-820. (1972) Zbl0249.35073MR0399675
  2. Biroli M., Sur la solution faible des inéquations d'évolution du type de Navier-Stokes avec convexe dépendant du temps, Boll. U. M. I., (4) 11 (1975), 309-321. (1975) Zbl0307.35074MR0420034
  3. Brézis H., 10.1016/0022-247X(72)90231-4, J. Math. Anal. Appl., 39 (1972), 159-165. (1972) Zbl0238.35068MR0312349DOI10.1016/0022-247X(72)90231-4
  4. Brézis H., Opérateurs maximaux monotones et semigroupes de contractions dans les escapes de Hilbert, Math. Studies 5, North Holland, 1973. (1973) Zbl0252.47055
  5. Ladyshenskaja O. A., On new equations for describing the motion of viscous, incompressible fluids and the global solvability of their boundary value problems, (Russian). Trudy Mat. Inst. Akad. Nauk SSSR, СII (1967), 85-104. (1967) 
  6. Ladyshenskaja O. A., On modifications of the Navier-Stokes equations with big gradient of velocity, (Russian). Zap. Nauch. Sem. Leningr. Ot. Mat. Inst., 7 (1968), 126-154. (1968) MR0241832
  7. Lions J. L., Quelques méthodes de résolution des problèmes aux limites non linéaires, Paris 1969. (1969) Zbl0189.40603MR0259693
  8. Prouse G., On a unilateral problem for the Navier-Stokes equations, Atti Accad. Naz. Lincei, Rend. Cl. Sci. Fis. Mat., (8) 62 (1972); Nota I: 337-342; Nota II: 467-478. (1972) Zbl0253.35067MR0342882
  9. Yosida K., Functional analysis, Berlin, Göttingen, Heidelberg 1965. (1965) Zbl0126.11504MR0180824

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