Weak/BV Stability and a-contraction in fluid dynamics

This paper introduces the a-contraction theory for the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> mml:msup mml:miL</mml:mi> mml:mn2</mml:mn> </mml:msup> </mml:math> 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 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathM