Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars
arXiv:0812.1110 · doi:10.1016/j.jmaa.2007.10.026
Abstract
We study the Euler-Poisson equations of describing the evolution of the gaseous star in astrophysics. Firstly, we construct a family of analytical blowup solutions for the isothermal case in R^2. Furthermore the blowup rate of the above solutions is also studied and some remarks about the applicability of such solutions to the Navier-Stokes-Poisson equations and the drift-diffusion model in semiconductors are included. Finally, for the isothermal case, the result of Makino and Perthame for the tame solutions is extended to show that the life span of such solutions must be finite if the initial data is with compact support.
15 pages
References in corpus (1)
Cited by in corpus (8)
- Analytical Solutions to the Navier-Stokes Equations
- Analytical Solutions to the Navier-Stokes Equations with Density-dependent Viscosity and with Pressure
- Analytical Blowup Solutions to the Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity in R^N
- Analytical Blowup Solutions to the Isothermal Euler-Poisson Equations of Gaseous Stars in R^N
- Analytical Blowup Solutions to the 4-dimensional Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity
- Analytical Blowup Solutions to the 3-dimensional Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity
- Blowup of C^2 Solutions for the Euler Equations and Euler-Poisson Equations in R^N
- Stabilities for Euler-Poisson Equations in Some Special Dimensions