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

Furioli, Giulia; Lemarié-Rieusset, Pierre-Gilles; Terraneo, Elide

C. R. Acad. Sci., Paris, Sér. I, Math. 325, No. 12, 1253-1256 (1997).

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