A note on the uniqueness of mild solutions to the Navier-Stokes equations

Abstract.

In this note, we will give another proof of the uniqueness of mild solutions to the Navier-Stokes equations in the class C([0,∞);$L^{d}(\mathbb {R}^{d})^{d})$ by a simple application of Giga-Shor’s L ^p − L ^q (time-space) estimates, i.e., integral norms in the time variable. The proof relies on a method introduced by S. Monniaux [9] to prove the same result.