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2016 ; 5
(ä): 196
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Perturbational blowup solutions to the compressible Euler equations with damping
#MMPMID27026892
Cheung KL
Springerplus
2016[]; 5
(ä): 196
PMID27026892
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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. METHOD: 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. CONCLUSION: 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.