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

E. Capelas de Oliveira; J. Vanterler da C. Sousa

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

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arxiv 1907.06587 v2 pith:MWZT3VDU submitted 2019-07-03 math.AP

J. Vanterler da C. Sousa , E. Capelas de Oliveira This is my paper · ORCID

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keywords leftmildrightequationsinequalitymathbbnavier-stokesresult

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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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Ulam-Hyers stabilities of mild solutions of the fractional nonlinear abstract Cauchy problem
math.CA 2019-08 conditional novelty 4.0 of 10

The authors prove Ulam-Hyers and Ulam-Hyers-Rassias stability for mild solutions of a Hilfer fractional abstract Cauchy problem on [0,T] and [0,∞) using the Banach fixed point theorem.

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