Dependence of Entropy Solutions in the Large for the Euler Equations on Nonlinear Flux Functions
Gui-Qiang Chen, Cleopatra Christoforou and Yongqian Zhang
Abstract: We study the dependence of entropy solutions in the large for hyperbolic systems of conservation laws whose flux functions depend on a parameter vector μ. We first formulate an effective approach for establishing the L1-estimate pointwise in time between entropy solutions for μ=0 and μ≠0, respectively, with respect to the flux parameter vector μ. Then we employ this approach and successfully establish the L1-estimate between entropy solutions in the large for several important nonlinear physical systems including the isentropic and relativistic Euler equations and for the isothermal Euler equations, respectively, for which the parameters are the adiabatic exponent γ>1 and the speed of light c<∞.