Czechoslovak Mathematical Journal, Vol. 71, No. 4, pp. 1189-1198, 2021
Blow-up for 3-D compressible isentropic Navier-Stokes-Poisson equations
Shanshan Yang, Hongbiao Jiang, Yinhe Lin
Received August 12, 2020. Published online June 28, 2021.
Abstract: We study compressible isentropic Navier-Stokes-Poisson equations in ${\mathbb R}^3$. With some appropriate assumptions on the density, velocity and potential, we show that the classical solution of the Cauchy problem for compressible unipolar isentropic Navier-Stokes-Poisson equations with attractive forcing will blow up in finite time. The proof is based on a contradiction argument, which relies on proving the conservation of total mass and total momentum.
Keywords: compressible isentropic Navier-Stokes-Poisson equation; unipolar; energy solution; blow-up
Affiliations: Shanshan Yang, School of Science, Zhejiang Sci-Tech University, 5 Second Avenue, Xiasha Higher Education Zone, Hangzhou 310018, P. R. China, e-mail: yss960501@163.com; Hongbiao Jiang, Yinhe Lin (corresponding author), Institute of Nonlinear Analysis and Department of Mathematics, Lishui University, Lishui 323000, P. R. China, e-mail: scumatlyh@163.com, lsxyhbj@126.com