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

In this note, we will give another proof of the uniqueness of mild solutions to the Navier-Stokes equations in the class C([0,∞);\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$L^{d}(\mathbb {R}^{d})^{d})$$ \end{document} by a simple application of Giga-Shor’s Lp − Lq (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.