Renormalized solutions for the Maxwell--Stefan system with an application to uniqueness of weak solutions

Abstract

We give conditions that guarantee uniqueness of renormalized solutions for the Maxwell-Stefan system. The proof is based on an identity for the evolution of the symmetrized relative entropy. Using the method of doubling the variables we derive the identity for two renormalized solutions and use information on the spectrum of the Maxwell-Stefan matrix to estimate the symmetrized relative entropy and show uniqueness. We then show that weak solutions for the Maxwell-Stefan system have sufficient regularity to produce renormalized solutions. Combining the two results yields a uniqueness result for weak solutions of the Maxwell-Stefan system with bounded fluxes.