2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/173744We study the 4-dimensional pressureless Navier--Stokes-Poisson equations with density-dependent viscosity. The analytical solutions with arbitrary time blowup, in radial symmetry, are constructed in this paper.8 pagesAnalysis of PDEsMathematical Physics35Q30, 76N10Analytical Blowup Solutions to the 4-dimensional Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscositytext