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On the uniqueness of mild solutions to the time-fractional Navier-Stokes equations in $L^{N} \left( \mathbb{R} ^{N}\right) ^{N} $ (1907.06587v2)

Published 3 Jul 2019 in math.AP

Abstract: In this paper, we present the result of maximum regularity of the mild solution of the fractional Cauchy problem. As our main result, we investigate the uniqueness of mild solutions for time-fractional Navier-Stokes equations in class $C\left([0,\infty);L{N}\left( \mathbb{R}{N}\right){N}\right)$ by means of the estimates $L{p}-L{q}$ of Giga-Shor inequality and the Gronwall inequality.

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