On the well-posedness of the full compressible Navier-Stokes system in critical Besov spaces

2014/07/17 by Chikami, Noboru, Danchin, Raphaël
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1407.4661

Abstract

We are concerned with the Cauchy problem of the full compressible Navier-Stokes equations satisfied by viscous and heat conducting fluids in ℝⁿ. We focus on the so-called critical Besov regularity framework. In this setting, it is natural to consider initial densities ρ₀, velocity fields u₀ and temperatures θ₀ with a₀:=ρ₀-1∈ B^{\frac np}_p,1, u₀∈ B^{\frac np-1}_p,1 and θ₀∈ B^{\frac np-2}_p,1. After recasting the whole system in Lagrangian coordinates, and working with the total energy along the flow rather than with the temperature, we discover that the system may be solved by means of Banach fixed point theorem in a critical functional framework whenever the space dimension is n≥2, and 1

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