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Archive for Rational Mechanics and Analysis

, Volume 189, Issue 1, pp 97–130 | Cite as

Continuous Dependence of Entropy Solutions to the Euler Equations on the Adiabatic Exponent and Mach Number

  • Gui-Qiang Chen
  • Cleopatra Christoforou
  • Yongqian Zhang
Article

Abstract

We establish the L1-estimates for continuous dependence of entropy solutions to the full Euler equations away from the vacuum on two physical parameters: the adiabatic exponent γ → 1 that passes from the non-isentropic to isothermal Euler equations and the Mach number \(\tt{M} \to 0\) that passes from the compressible to incompressible Euler equations. Our analysis involves the effective approach developed in our earlier work and additional new techniques that generalize this approach to the setting of the full Euler equations.

Keywords

Mach Number Euler Equation Shock Front Continuous Dependence Entropy Solution 

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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Gui-Qiang Chen
    • 1
    • 2
  • Cleopatra Christoforou
    • 2
    • 3
  • Yongqian Zhang
    • 4
  1. 1.School of Mathematical SciencesFudan UniversityShanghaiPeople’s Republic of China
  2. 2.Department of MathematicsNorthwestern UniversityEvanstonUSA
  3. 3.Department of MathematicsUniversity of HoustonHoustonUSA
  4. 4.School of Mathematical Sciences and Key Laboratory of Mathematics for Nonlinear Sciences (Ministry of Education)Fudan UniversityShanghaiPeople’s Republic of China

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