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A Stokes-type problem for a viscoelastic model of salt rocks is considered, and existence, uniqueness and regularity are investigated in the scale of L2-based Sobolev spaces. The system is transformed into a generalized Stokes problem, and the proper conditions on the parameters of the model that guarantee that the system is uniformly elliptic are given. Under those conditions, existence, uniqueness and low-order regularity are obtained under classical regularity conditions on the data, while higher-order regularity is proved under less stringent conditions than classical ones. Explicit estimates for the solution in terms of the data are given accordingly. [ABSTRACT FROM AUTHOR]

Existence and asymptotic behavior of nonlinear evolution equations with memory in the maximal order term, driven by additive or multiplicative Wiener stochastic processes, are studied. Examples include the nonlinear stochastic heat and diffusion equations with memory, viscoelastic fluid equations and the stochastic porous media equations with memory. [ABSTRACT FROM AUTHOR]