On uniqueness for bounded channel flows of viscoelastic fluids

Marshall J. Leitman; Epifanio G. Virga

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti (1988)

  • Volume: 82, Issue: 4, page 717-723
  • ISSN: 0392-7881

Abstract

top
It was conjectured in [1] that there is at most one bounded channel flow for a viscoelastic fluid whose stress relaxation function G is positive, integrable, and strictly convex. In this paper we prove the uniqueness of bounded channel flows, assuming G to be non-negative, integrable, and convex, but different from a very specific piecewise linear function. Furthermore, whenever these hypotheses apply, the unbounded channel flows, if any, must grow in time faster than any polynomial.

How to cite

top

Leitman, Marshall J., and Virga, Epifanio G.. "On uniqueness for bounded channel flows of viscoelastic fluids." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti 82.4 (1988): 717-723. <http://eudml.org/doc/289169>.

@article{Leitman1988,
abstract = {It was conjectured in [1] that there is at most one bounded channel flow for a viscoelastic fluid whose stress relaxation function $G$ is positive, integrable, and strictly convex. In this paper we prove the uniqueness of bounded channel flows, assuming $G$ to be non-negative, integrable, and convex, but different from a very specific piecewise linear function. Furthermore, whenever these hypotheses apply, the unbounded channel flows, if any, must grow in time faster than any polynomial.},
author = {Leitman, Marshall J., Virga, Epifanio G.},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti},
keywords = {Uniqueness; Channel flows; Viscoelasticy fluids},
language = {eng},
month = {12},
number = {4},
pages = {717-723},
publisher = {Accademia Nazionale dei Lincei},
title = {On uniqueness for bounded channel flows of viscoelastic fluids},
url = {http://eudml.org/doc/289169},
volume = {82},
year = {1988},
}

TY - JOUR
AU - Leitman, Marshall J.
AU - Virga, Epifanio G.
TI - On uniqueness for bounded channel flows of viscoelastic fluids
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
DA - 1988/12//
PB - Accademia Nazionale dei Lincei
VL - 82
IS - 4
SP - 717
EP - 723
AB - It was conjectured in [1] that there is at most one bounded channel flow for a viscoelastic fluid whose stress relaxation function $G$ is positive, integrable, and strictly convex. In this paper we prove the uniqueness of bounded channel flows, assuming $G$ to be non-negative, integrable, and convex, but different from a very specific piecewise linear function. Furthermore, whenever these hypotheses apply, the unbounded channel flows, if any, must grow in time faster than any polynomial.
LA - eng
KW - Uniqueness; Channel flows; Viscoelasticy fluids
UR - http://eudml.org/doc/289169
ER -

References

top
  1. LEITMAN, M.J. and VIRGA, E.G. (1988) - On bounded channel flows of viscoelastic fluids, «Atti Acc. Lincei Rend. fis.», 82,291-291. Zbl0714.76013MR1152648
  2. CAPRIZ, G. and VIRGA, E.G. (1988) - Un teorema di unicità in viscoelasticità lineare, «Rend. Sem. Mat. Univ. Padova», 79, 15-24. Zbl0655.73020MR964016
  3. VERGARA CAFFARELLI, G. and VIRGA, E.G. (1987) - Sull'unicità della soluzione del problema dinamico della viscoelasticità lineare, «Atti Acc. Lincei Rend. fis.», 81, 379-387. Zbl0667.73027MR999829
  4. JOSEPH, D.D., RENARDY, M. and SAUT, J.C. (1984-85) - Hyperbolicity and change of type in the flow of viscoelastic fluids, «Arch. Rational Mech. Anal.», 87, 213-251. Zbl0572.76011MR768067DOI10.1007/BF00250725
  5. HALE, J. (1971) - Functional differential equations, «Springer Verlag, Berlin», etc. Zbl0222.34003MR390425
  6. LEITMAN, M.J. and MIZEL, V.J. (1974) - On fading memory spaces and hereditary integral equations, «Arch. Rational Mech. Anal.», 75, 18-51. Zbl0297.45001MR367734

NotesEmbed ?

top

You must be logged in to post comments.