Dependence of entropy solutions in the large for the Euler equations on nonlinear flux functions Gui-Qiang ChenCleopatra ChristoforouYong Qian Zhang 35L6535L6735B3076N1576Y0535B3583A05dependencenonlinear flux functionsEuler equationsentropy solutionsadiabiatic exponentlight speedisothermalisentropicrelativistic$L$^1-estimateerror estimatefront-tracking We study the dependence of entropy solutions in the large for hyperbolic systems of conservation laws whose flux functions depend on a parameter vector $\mu$. We first formulate an effective approach for establishing the $L^1$-estimate pointwise in time between entropy solutions for $\mu \ne 0$ and $\mu = 0$, respectively, with respect to the flux parameter vector $\mu$. 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 $\gamma > 1$ and the speed of light $c < \infty$. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3063 10.1512/iumj.2007.56.3063 en Indiana Univ. Math. J. 56 (2007) 2535 - 2568 state-of-the-art mathematics http://iumj.org/access/