title: Blowup phenomena for the compressible euler and euler-poisson equations with initial functional conditions.
abstract: We study, in the radial symmetric case, the finite time life span of the compressible Euler or Euler-Poisson equations in R (N) . For time t ≥ 0, we can define a functional H(t) associated with the solution of the equations and some testing function f. When the pressure function P of the governing equations is of the form P = Kρ (γ) , where ρ is the density function, K is a constant, and γ > 1, we can show that the nontrivial C (1) solutions with nonslip boundary condition will blow up in finite time if H(0) satisfies some initial functional conditions defined by the integrals of f. Examples of the testing functions include r (N-1)ln(r + 1), r (N-1) e (r) , r (N-1)(r (3) - 3r (2) + 3r + ε), r (N-1)sin((π/2)(r/R)), and r (N-1)sinh r. The corresponding blowup result for the 1-dimensional nonradial symmetric case is also given.
authors: Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong.
authors: Sen
authors: 0000-0003-0302-0747
authors: S
authors: Wong
authors: Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories, Hong Kong.
authors: Manwai
authors: 0000-0002-5035-3555
authors: M
authors: Yuen
mesh_terms: D003198:Computer Simulation; D008962:Models, Theoretical