In this paper we study the quasi-static problem for a viscoelastic fluid by means of the concept of minimal state. This implies the use of a different free energy defined in a wider space of data. The existence and uniqueness is proved in this new space and the asymptotic decay for the problem with non vanishing supplies is obtained for a large class of memory kernels, including those presenting an exponential or polynomial decay. © 2011 Elsevier Ltd. All rights reserved.
Fabrizio, M., Lazzari, B., & Nibbi, R. (2012). On the asymptotic behavior of the quasi-static problem for a linear viscoelastic fluid. Applied Mathematics Letters, 25(10), 1464–1469. https://doi.org/10.1016/j.aml.2011.12.025