# Preprint 2006-027

# 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 *L*^{1}-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 *L*^{1}-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*<∞.