Unicité dans L3(R3) et d'autres espaces fonctionnels limites pour Navier-Stokes.

By Giulia Furioli, P. Lemarié-Rieusset, E. Terraneo. 2000

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The Navier-Stokes equations and weak Herz spaces (2011, background): “As for uniqueness of global-in-time mild solution, in the case u0 ∈ L(3)(R(3)), it is well-known that the solution is unique in the class C([0, T ); L(3)) even if initial data is large, see [18], [19] and [39].”
An alternative approach to regularity for the Navier–Stokes equations in critical spaces (2009, background): “At this point, we also mention the following uniqueness theorem for solutions in the class C([0, T );L3) established in [17] (see also [45] for a simplified proof):”
Wild solutions of the Navier–Stokes equations whose singular sets in time have Hausdorff dimension strictly less than 1 (2018, result): “Similar weak-strong uniqueness results hold within the class of mild solutions, except the q = 3 endpoint which requires continuity in time [13, 16, 34].”
Convex integration and phenomenologies in turbulence (2019, background): “the solution is bounded in a space LptL q x for 2/p+ 3/q ≤ 1 [111, 161, 175, 104, 72, 85, 135, 126, 119].”