Some applications of the SBV Regularity Theorem for entropy solutions of 1D scalar conservation laws to Convection Theory and sticky particles
Received: 7 October 2010
Accepted: 17 December 2010
Mathematics Subject Classification (2000): 35L65, 35D10, 35Q35.
Keywords: SBV regularity, pressureless gasses, sticky particles, Convection Theory, Generalized Hydrostatic Boussinesq equations, Hamilton-Jacobi equations, scalar conservation laws.
Abstract: We show how it is possible to apply the SBV Regularity Theorem for entropy solutions of one-dimensional scalar conservation laws, proved by Ambrosio and De Lellis, to Convection Theory and sticky particles. In the multi-dimensional case we present a counterexample which prevent us from using the same approach.