title: Perturbational blowup solutions to the compressible Euler equations with damping.
abstract: BACKGROUND
  The N-dimensional isentropic compressible Euler system with a damping term is one of the most fundamental equations in fluid dynamics. Since it does not have a general solution in a closed form for arbitrary well-posed initial value problems. Constructing exact solutions to the system is a useful way to obtain important information on the properties of its solutions.
  
  
  METHODS
  In this article, we construct two families of exact solutions for the one-dimensional isentropic compressible Euler equations with damping by the perturbational method. The two families of exact solutions found include the cases [Formula: see text] and [Formula: see text], where [Formula: see text] is the adiabatic constant.
  
  
  RESULTS
  With analysis of the key ordinary differential equation, we show that the classes of solutions include both blowup type and global existence type when the parameters are suitably chosen. Moreover, in the blowup cases, we show that the singularities are of essential type in the sense that they cannot be smoothed by redefining values at the odd points.
  
  
  CONCLUSIONS
  The two families of exact solutions obtained in this paper can be useful to study of related numerical methods and algorithms such as the finite difference method, the finite element method and the finite volume method that are applied by scientists to simulate the fluids for applications.
authors.affiliation: Department of Mathematics and Information Technology, The Hong Kong Institute of Education, 10 Lo Ping Road, Tai Po, New Territories Hong Kong.
authors.forename: Ka Luen
authors.identifier: 0000-0003-4107-7840
authors.initials: KL
authors.lastname: Cheung
keywords: Blowup; Damping; Euler equations; Global existence; Perturbational method; Singularity