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We consider the nonstationary Navier-Stokes system in a smooth bounded domain Ω ⊂ R 3 with initial value u 0 ∈ L 2 σ (Ω). It is an important question to determine the optimal initial value condition in order to prove the existence of a unique local strong solution satisfying Serrin's condition. In this paper, we introduce a weighted Serrin condition that yields a necessary and sufficient initial value condition to guarantee the existence of local strong solutions u(·) contained in the weighteddoi:10.1619/fesi.59.199 fatcat:dfpwnuax7raoxil435dt7qfr7q