## 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

### Keywords:

uniqueness; mild solutions; Navier-Stokes equations
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