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.
@article{bwmeta1.element.bwnjournal-article-bcpv27z2p367bwm,
author = {Prouse, Giovanni},
title = {On a Navier-Stokes type equation and inequality},
journal = {Banach Center Publications},
volume = {27},
year = {1992},
pages = {367-371},
zbl = {0787.35068},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z2p367bwm}
}
Prouse, Giovanni. On a Navier-Stokes type equation and inequality. Banach Center Publications, Tome 27 (1992) pp. 367-371. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv27z2p367bwm/
[000] [1] L. Amerio and G. Prouse, Almost-periodic Functions and Functional Equations, Van Nostrand, 1971. | Zbl 0215.15701
[001] [2] T. Collini, On a Navier-Stokes type inequality, Rend. Ist. Lomb. Sc. Lett., to appear. | Zbl 0754.35108
[002] [3] T. Collini, Periodic solutions of a Navier-Stokes type inequality, ibid., to appear. | Zbl 0754.35109
[003] [4] P. Grisvard, Elliptic Problems in Nonsmooth Domains, Pitman, 1985. | Zbl 0695.35060
[004] [5] A. Iannelli, Bounded and almost-periodic solutions of a Navier-Stokes type equation, Rend. Accad. Naz. Sci. XL, to appear. | Zbl 0833.35108
[005] [6] G. Prodi, Un teorema di unicità per le equazioni di Navier-Stokes, Ann. Mat. Pura Appl. 48 (1959), 173-182.
[006] [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.