In this paper, we study an inverse problem for the nonstationary Stokes system in a bounded domain Ω with a nonlinear integral overdetermination condition, describing the kinetic energy E(t) of the fluid. We construct two classes of solutions: weak and very weak. In the case where the kinetic energy E belongs to W21(0,T), we construct weak solutions. If E belongs only to L2(0,T), we construct very weak solutions.
Bačianskas et al. (Wed,) studied this question.
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