Abstract: Compressible Euler equations are a typical system of hyperbolic conservation laws, whose solution forms shock waves in general. It is well known that global BV solutions of system of hyperbolic conservation laws exist, when one considers small BV initial data.
In this talk, I will first discuss the join work with Krupa and Vasseur for systems with two unknowns and non-isentropic Euler equations with three unknowns, where we established an L2 stability theory using the method of relative entropy on modified front tracking scheme.
Then I will introduce the recent proof on the vanishing viscosity limit from Navier-Stokes equations to the unique BV solution of compressible Euler equations. This is a famous open problem after Bressan-Bianchini’s seminal vanishing artificial viscosity limit result for BV solutions of hyperbolic conservation laws. This is a join work with Kang and Vasseur.
