Global existence for viscous systems of conservation laws in $L^p$ framework

Abstract

In this paper, which originates from Chapter 4 of the author's PhD thesis [1, Chap. 4], we investigate the global well-posedness of a class of partially diffusive hyperbolic systems in critical homogeneous Besov spaces. Our main objective is to extend the analysis developed in our previous work [2] to a functional framework in which the high-frequency com- ponents of the solution are controlled in $L^p$-based spaces with $p > 2$. This broader framework allows us to establish global existence under weaker smallness assumptions on the initial data and provides more precise information on the qualitative behavior of the resulting solutions. In particular, our analysis yields refined regularity. As an application, our global existence theorem applies to the multidimensional compressible Fourier-Navier-Stokes system