A new construction of weak solutions to compressible Navier-Stokes equations

2022/11/22 by Chaudhuri, Nilasis, Mucha, Piotr B., Zatorska, Ewelina · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2211.12189

Abstract

We prove the existence of the weak solutions to the compressible Navier--Stokes system with barotropic pressure p(\varrho)=\varrho^γ for γ≥ 9/5 in three space dimension. The novelty of the paper is the approximation scheme that instead of the classical regularization of the continuity equation (based on the viscosity approximation \ep Δ\varrho) uses more direct truncation and regularisation of nonlinear terms an the pressure. This scheme is compatible with the Bresch-Jabin compactness criterion for the density. We revisit this criterion and prove, in full rigour, that it can be applied in our approximation at any level.

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• Global weak solutions and incompressible limit to the isentropic compressible Navier-Stokes equations in the half-plane with ripped density and large initial data

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