Self-Similar Solutions to the Spherically-Symmetric Euler Equations with a Two-Constant Equation of State

Qitao Zhang () and Yanbo Hu ()
Additional contact information
Qitao Zhang: Hangzhou Normal University
Yanbo Hu: Hangzhou Normal University

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 1, 35-49

Abstract: Abstract This paper is concerned with self-similar flows of the multidimensional isentropic compressible Euler equations caused by the uniform expansion of a spherically-symmetric piston into the undisturbed fluid. Under the spherically-symmetric and self-similar assumptions, the problem can be reduced to a boundary value problem for a system of nonlinear ordinary differential equations. We consider the two-constant equation of state $$p = {A_1}{\rho ^{\gamma 1}} + {A_2}{\rho ^{\gamma 2}}$$ p = A 1 ρ γ 1 + A 2 ρ γ 2 which arises in a number of various physical contexts and results the problem becomes more complicated than the case of polytropic gas equation of state. To deal with the difficulty, we first establish the global existence of smooth solutions to the boundary value problem for a new ODE system.

Keywords: Euler equations; spherically-symmetric flows; self-similar solutions; shock wave (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s13226-019-0305-z Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:indpam:v:50:y:2019:i:1:d:10.1007_s13226-019-0305-z

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/13226

DOI: 10.1007/s13226-019-0305-z

Access Statistics for this article

Indian Journal of Pure and Applied Mathematics is currently edited by Nidhi Chandhoke

More articles in Indian Journal of Pure and Applied Mathematics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().