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On uniqueness for bounded channel flows of viscoelastic fluids

Marshall J. LeitmanEpifanio G. Virga — 1988

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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.

On bounded channel flows of viscoelastic fluids

Marshall J. LeitmanEpifanio G. Virga — 1988

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that the smooth bounded channel flows of a viscoelastic fluid exhibit the following qualitative feature: Whenever the channel is sufficiently wide, any bounded velocity field satisfying the homogeneous equation of motion is such that if the flow stops at some time, then the flow is never unidirectional throughout the channel. We first demonstrate the qualitative property of the bounded channel flows. Then we show explicitly how a piecewise linear approximation of a relaxation function can...

On bounded channel flows of viscoelastic fluids

Marshall J. LeitmanEpifanio G. Virga — 1988

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

We show that the smooth bounded channel flows of a viscoelastic fluid exhibit the following qualitative feature: Whenever the channel is sufficiently wide, any bounded velocity field satisfying the homogeneous equation of motion is such that if the flow stops at some time, then the flow is never unidirectional throughout the channel. We first demonstrate the qualitative property of the bounded channel flows. Then we show explicitly how a piecewise linear approximation of a relaxation function can...

On uniqueness for bounded channel flows of viscoelastic fluids

Marshall J. LeitmanEpifanio G. Virga — 1988

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

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.

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