Genetic variations in the COVID19 virus are one of the main causes of the COVID19 pandemic outbreak in 2020 and 2021. In this article, we aim to introduce a new type of model, a system coupled with ordinary differential equations (ODEs) and measure differential equation (MDE), stemming from the classical SIR model for the variants distribution. Specifically, we model the evolution of susceptible
This paper studies a family of generalized surface quasigeostrophic (SQG) equations for an active scalar
 Award ID(s):
 1818754
 Publication Date:
 NSFPAR ID:
 10337310
 Journal Name:
 Communications on Pure & Applied Analysis
 Volume:
 0
 Issue:
 0
 Page Range or eLocationID:
 0
 ISSN:
 15340392
 Sponsoring Org:
 National Science Foundation
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and removed\begin{document}$ S $\end{document} populations by ODEs and the infected\begin{document}$ R $\end{document} population by a MDE comprised of a probability vector field (PVF) and a source term. In addition, the ODEs for\begin{document}$ I $\end{document} and\begin{document}$ S $\end{document} contains terms that are related to the measure\begin{document}$ R $\end{document} . We establish analytically the wellposedness of the coupled ODEMDE system by using generalized Wasserstein distance. We give two examples to show that the proposed ODEMDE model coincides with the classical SIR model in case of constant or timedependent parameters as special cases.\begin{document}$ I $\end{document} 
Abstract A longstanding problem in mathematical physics is the rigorous derivation of the incompressible Euler equation from Newtonian mechanics. Recently, HanKwan and Iacobelli (Proc Am Math Soc 149:3045–3061, 2021) showed that in the monokinetic regime, one can directly obtain the Euler equation from a system of
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