Global existence for systems of parabolic conservation laws in several space variables

Abstract

We prove the global existence of solutions of the Cauchy problem for certain systems of conservation laws with artificial viscosity terms added. The system is assumed to admit a quadratic entropy which is consistent with the viscosity matrix, and the initial data is assumed to be close to a constant in L 2 ∩ L ∞. In particular, our result applies to the equations of compressible fluid flow in two and three space variables.