Open AccessGlobal solutions to the non-local Navier-Stokes equations
Author(s) -
Joelma Azevedo,
Juan C. Pozo,
Arlúcio Viana
Publication year - 2022
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021146
Subject(s) - mathematics , context (archaeology) , navier–stokes equations , divergence (linguistics) , space (punctuation) , physics , computer science , compressibility , paleontology , linguistics , philosophy , biology , operating system , thermodynamics
This paper is devoted to the study of the global well-posedness for a non-local-in-time Navier-Stokes equation. Our results recover in particular other existing well-posedness results for the Navier-Stokes equations and their time-fractional version. We show the appropriate manner to apply Kato's strategy and this context, with initial conditions in the divergence-free Lebesgue space \begin{document}$ L^\sigma_d(\mathbb{R}^d) $\end{document} . Temporal decay at \begin{document}$ 0 $\end{document} and \begin{document}$ \infty $\end{document} are obtained for the solution and its gradient.