We consider the energy-critical focusing wave equation in space dimension $$N\ge 3$$ . The has a nonzero radial stationary solution W, which is unique up to scaling and sign change. It conjectured (soliton resolution) that any radial, bounded energy norm of equation, behaves asymptotically as sum modulated Ws, decoupled by scaling, radiation term. A nonradiative definition exterior $$\{|x|>|t|\...

<p style='text-indent:20px;'>We study the small data global regularity problem of <inline-formula><tex-math id="M2">\begin{document}$ 3D $\end{document}</tex-math></inline-formula> Vlasov-Poisson system for both relativistic case and non-relativistic case. The main goal this paper is twofold. (i) Based on a Fourier method, which works systematically case, we give s...