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Well-chosen weak solutions of the instationary Navier-Stokes system and their uniqueness. (English) Zbl 1397.35170
Authors’ abstract: We clarify the notion of well-chosen weak solutions of the instationary Navier-Stokes system recently introduced by the authors and P.-Y. Hsu in the article Initial values for the Navier-Stokes equations in spaces with weights in time, [Funkc. Ekvacioj, Ser. Int. 59, No. 2, 199–216 (2016; Zbl 1364.35236)]. Well-chosen weak solutions have initial values in \(L^{2}_{\sigma}(\Omega)\) contained also in a quasi-optimal scaling-invariant space of Besov type such that nevertheless Serrin’s Uniqueness Theorem cannot be applied. However, we find universal conditions such that a weak solution given by a concrete approximation method coincides with the strong solution in a weighted function class of Serrin type.

35Q30 Navier-Stokes equations
35B65 Smoothness and regularity of solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
35D30 Weak solutions to PDEs
35D35 Strong solutions to PDEs
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