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On the first problem of Stokes for Burgers’ fluids. I: Case \(\gamma <\lambda^2/4\). (English) Zbl 1163.76333

Summary: The velocity field and the associated tangential stress corresponding to the flow of a Burgers’ fluid over a suddenly moved flat plate are determined when the relaxation times satisfy the condition \(\gamma <\lambda ^{2}/4\). Using the Laplace transform, only one initial condition has been necessary for velocity. The well-known solutions for a Newtonian fluid, as well as those corresponding to an Oldroyd-B fluid performing the same motion, are obtained as limiting cases of our solutions.

MSC:

76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
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