Zusammenfassung: Es wird das Stabilit~itsverhalten eines Maxwell-Fluids in einer einfachen ebenen Scherstr6mung ftir eine spezielle St6rungsklasse untersucht. Notwendige und hinreichende Stabilitatskriterien sowie eine kritische Weissenbergzahl (Wek ~ 4) werden angegeben. Die Ergebnisse der Analyse stehen mit experimentellen Befunden in qualitativer Obereinstimmung.Abstract." The stability behaviour of a Maxwell fluid in a simple plane shear flow for a class of special perturbations is investigated. Necessary and sufficient stability criteria, especially a critical Weissenberg number for the stability (Wek ~ 4) are given. The results of the analysis are in qualitative agreement with experimental observations.
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