On a Navier-Stokes type equation and inequality

Giovanni Prouse

Banach Center Publications (1992)

  • Volume: 27, Issue: 2, page 367-371
  • ISSN: 0137-6934

Abstract

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A Navier-Stokes type equation corresponding to a non-linear relationship between the stress tensor and the velocity deformation tensor is studied and existence and uniqueness theorems for the solution, in the 3-dimensional case, of the Cauchy-Dirichlet problem, for a bounded solution and for an almost periodic solution are given. An inequality which in some sense is the limit of the equation is also considered and existence theorems for the solution of the Cauchy-Dirichlet problems and for a periodic solution are stated.

How to cite

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Prouse, Giovanni. "On a Navier-Stokes type equation and inequality." Banach Center Publications 27.2 (1992): 367-371. <http://eudml.org/doc/262743>.

@article{Prouse1992,
abstract = {A Navier-Stokes type equation corresponding to a non-linear relationship between the stress tensor and the velocity deformation tensor is studied and existence and uniqueness theorems for the solution, in the 3-dimensional case, of the Cauchy-Dirichlet problem, for a bounded solution and for an almost periodic solution are given. An inequality which in some sense is the limit of the equation is also considered and existence theorems for the solution of the Cauchy-Dirichlet problems and for a periodic solution are stated.},
author = {Prouse, Giovanni},
journal = {Banach Center Publications},
keywords = {Navier-Stokes type equation; existence; uniqueness; Cauchy-Dirichlet problem; bounded solution; almost periodic solution; inequality; periodic solution},
language = {eng},
number = {2},
pages = {367-371},
title = {On a Navier-Stokes type equation and inequality},
url = {http://eudml.org/doc/262743},
volume = {27},
year = {1992},
}

TY - JOUR
AU - Prouse, Giovanni
TI - On a Navier-Stokes type equation and inequality
JO - Banach Center Publications
PY - 1992
VL - 27
IS - 2
SP - 367
EP - 371
AB - A Navier-Stokes type equation corresponding to a non-linear relationship between the stress tensor and the velocity deformation tensor is studied and existence and uniqueness theorems for the solution, in the 3-dimensional case, of the Cauchy-Dirichlet problem, for a bounded solution and for an almost periodic solution are given. An inequality which in some sense is the limit of the equation is also considered and existence theorems for the solution of the Cauchy-Dirichlet problems and for a periodic solution are stated.
LA - eng
KW - Navier-Stokes type equation; existence; uniqueness; Cauchy-Dirichlet problem; bounded solution; almost periodic solution; inequality; periodic solution
UR - http://eudml.org/doc/262743
ER -

References

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  1. [1] L. Amerio and G. Prouse, Almost-periodic Functions and Functional Equations, Van Nostrand, 1971. Zbl0215.15701
  2. [2] T. Collini, On a Navier-Stokes type inequality, Rend. Ist. Lomb. Sc. Lett., to appear. Zbl0754.35108
  3. [3] T. Collini, Periodic solutions of a Navier-Stokes type inequality, ibid., to appear. Zbl0754.35109
  4. [4] P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, 1985. Zbl0695.35060
  5. [5] A. Iannelli, Bounded and almost-periodic solutions of a Navier-Stokes type equation, Rend. Accad. Naz. Sci. XL, to appear. Zbl0833.35108
  6. [6] G. Prodi, Un teorema di unicità per le equazioni di Navier-Stokes, Ann. Mat. Pura Appl. 48 (1959), 173-182. 
  7. [7] G. Prouse, On a Navier-Stokes type equation, in: Non-linear Analysis: a Tribute to G. Prodi, Quaderni Scuola Norm. Sup. Pisa, to appear. 

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