Analytical Blowup Solutions to the 4-dimensional Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity

TL;DR

This paper constructs analytical solutions that exhibit finite-time blowup for the 4-dimensional pressureless Navier-Stokes-Poisson equations with density-dependent viscosity, providing insights into singularity formation in such systems.

Contribution

It introduces explicit analytical solutions demonstrating finite-time blowup in a 4D pressureless Navier-Stokes-Poisson model with density-dependent viscosity, a novel contribution in higher-dimensional fluid dynamics.

Findings

Explicit blowup solutions in 4D with radial symmetry

Demonstration of finite-time singularity formation

Advancement in understanding pressureless fluid models

Abstract

We 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.