Viscous System of Conservation Laws: Singular Limits

Abstract. We continue our analysis of the Cauchy problem for viscous system of conservation, under natural assumptions. We examine in which way does the existence time depend upon the viscous tensor B(u). In particular, we consider singular limits, where the rank of the symbol B(u; ξ) drops at the limit. This covers a lot of situations, for instance that of the limit of the Navier-Stokes-Fourier system towards the EulerFourier system, or that of the vanishing viscosity. We emphasize the symmetry of the dissipation tensor, an hypothesis which is reminiscent to the Onsager’s reciprocity relations. We find it useful in this asymptotic context, when establishing uniform estimates.