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Here we investigate global strong solutions for a class of partiallydissipative hyperbolic systems in the framework of critical homogeneous Besovspaces. Our primary goal is to extend the analysis of our previous paper [10]to a functional framework where the low frequencies of the solution are onlybounded in L p-type spaces with p larger than 2. This enables us to prescribeweaker smallness conditions for global well-posedness and to get a moreaccurate information on the qualitative properties of the constructedsolutions. Our existence theorem in particular applies to the multi-dimensionalisentropic compressible Euler system with relaxation, and provide us withbounds that are independent of the relaxation parameter. As a consequence, wejustify rigorously the relaxation limit to the porous media equation andexhibit explicit rates of convergence for suitable norms, a completely newresult to the best of our knowledge.

Global existence for partially dissipative hyperbolic systems in the Lp framework, and relaxation limit