Global Well-posedness and Optimal Decay Rate of the Quasi-static Incompressible Navier–Stokes–Fourier–Maxwell–Poisson System

This work aims to establish global classical solution and optimal \begin{document}$ L^p $\end{document} ( \begin{document}$ p\ge 2 $\end{document} ) time decay rate of the quasi-static incompressible Navier–Stokes–Fourier–Maxwell–Poisson system with small initial data in \begin{document}$ \mathbb{R}^3 $\end{document} . The optimal \begin{document}$ L^2 $\end{document} time decay rate for higher order spatial derivatives is also given. To deal with the difficulty induced by the degeneration of the coupled Maxwell equation, we adopt the vector-valued form of the electric field \begin{document}$ E $\end{document} to obtain the time decay rate.