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The weak connectedness of the attainability set of weak solutions of the three-dimensional Navier-Stokes equations. (English) Zbl 1143.35082
In the present study, the authors show that the Kueser property holds for the weak solutions of the three-dimensional Navier-Stokes equations (NSE) satisfying the energy inequality in a bounded domain by using the weak topology of the phase space. Moreover, the authors show that the weak global attractor in the phase space of the set-valued dynamical system generated by the weak solutions of the NSE is connected in the phase space endowed by the weak topology.

MSC:
35Q30Stokes and Navier-Stokes equations
37C30Functional analytic techniques in dynamical systems
37N10Dynamical systems in fluid mechanics, oceanography and meteorology
76D05Navier-Stokes equations (fluid dynamics)
76D03Existence, uniqueness, and regularity theory