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On the uniqueness in \(L^3(\mathbb{R}^3)\) of mild solutions for the Navier-Stokes equations. (Sur l’unicité dans \(L^3(\mathbb{R}^3)\) des solutions “mild” des équations de Navier-Stokes.) (French) Zbl 0894.35083

Summary: We prove uniqueness in \(L^3(\mathbb{R}^3)\) for mild solutions of the Navier-Stokes equations when the initial data are small enough. The proof is based on an estimate in the \(\dot B^{1/2,\infty}_2(\mathbb{R}^3)\) norm for the bilinear term.

MSC:

35Q30 Navier-Stokes equations
35D99 Generalized solutions to partial differential equations
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