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 (23)
- Analytical Solutions to the Navier-Stokes Equations
- Self-Similar Solutions with Elliptic Symmetry for the Compressible Euler and Navier-Stokes Equations in R^{N}
- Vortical and Self-similar Flows of 2D Compressible Euler Equations
- Blowup for the Euler and Euler-Poisson Equations with Repulsive Forces
- Analytical Solutions to the Navier-Stokes Equations with Density-dependent Viscosity and with Pressure
- Rotational and Self-similar Solutions for the Compressible Euler Equations in R^3
- Some Exact Blowup Solutions to the Pressureless Euler Equations in R^N
- Analytical Blowup Solutions to the Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity in R^N
- Periodic Solutions of 2D Isothermal Euler-Poisson Equations with Possible Applications to Spiral and Disk-like Galaxies
- Blowup for the C^1 Solutions of the Euler-Poisson Equations of Gaseous Stars in R^N
- Self-Similar Blowup Solutions to the 2-Component Camassa-Holm Equations
- Self-Similar Blowup Solutions to the 2-Component Degasperis-Procesi Shallow Water System
- Analytical Solutions to the Navier-Stokes-Poisson Equations with Density-dependent Viscosity and with Pressure
- Perturbational Blowup Solutions to the 2-Component Camassa-Holm Equations
- Analytical Blowup Solutions to the 2-dimensional Isothermal Euler-Poisson Equations of Gaseous Stars II
- Analytical Blowup Solutions to the Isothermal Euler-Poisson Equations of Gaseous Stars in R^N
- Blowup for Solutions of the N-dimensional Euler-Poisson Equations in Newtonian Cosmology
- Analytical Blowup Solutions to the 3-dimensional Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity
- Analytical Blowup Solutions to the 4-dimensional Pressureless Navier-Stokes-Poisson Equations with Density-dependent Viscosity
- Stabilities for Euler-Poisson Equations in Some Special Dimensions
- Line Solutions for the Euler and Euler-Poisson Equations with Multiple Gamma Law
- Blowup of C^2 Solutions for the Euler Equations and Euler-Poisson Equations in R^N
- Blow-up of Smooth Solutions to the Euler-Poisson Equations