Weak/BV Stability and a-contraction in fluid dynamics

This paper introduces the a-contraction theory for the L 2 stability of discontinuous solutions to conservation laws and their inviscid limits. It can be viewed as an extension of the Weak–Strong stability principle, first introduced by Dafermos and DiPerna, to the stability of discontinuous solutions–e.g. bounded in B V –among general weak entropic solutions. For example, small BV solutions to barotropic Euler equations can be obtained as inviscid limits of solutions to the associated compressible Navier–Stokes equations. In the barotropic setting, this extends the celebrated work of Bianchini and Bressan to models with physical viscosity.