Uniform stability of the relativistic Cucker-Smale model and its application to a mean-field limit

<p style='text-indent:20px;'>We present a uniform(-in-time) stability of the relativistic Cucker-Smale (RCS) model in suitable framework and study its application to uniform mean-field limit which lifts earlier classical results for CS setting. For this, we first provide sufficient an exponential flocking RCS terms diameters state observables, coupling strength communication weight function, then use obtained estimate derive <inline-formula><tex-math id="M1">\begin{document}$ \ell_{q,p} $\end{document}</tex-math></inline-formula>-stability under appropriate conditions on initial data system parameters. As derived id="M2">\begin{document}$ estimate, show that can be made some admissible class solutions uniformly time. This justifies formal derivation kinetic equation [<xref ref-type="bibr" rid="b18">18</xref>] rigorous setting.</p>