Some new well-posedness results for continuity and transport equations, and applications to the chromatography system

2009/04/02 by Luigi Ambrosio, Gianluca Crippa, Ambrosio, Luigi +5
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.0904.0359

33 pages, minor changes

arxiv created 2009/10/01 · arxiv updated 2009/12/01

Abstract

We obtain various new well-posedness results for continuity and transport equations, among them an existence and uniqueness theorem (in the class of strongly continuous solutions) in the case of nearly incompressible vector fields, possibly having a blow-up of the BV norm at the initial time. We apply these results (valid in any space dimension) to the k x k chromatography system of conservation laws and to the k x k Keyfitz and Kranzer system, both in one space dimension.

Related

• On the one-dimensional continuity equation with a nearly incompressible vector field
• Well-posedness for the continuity equation for vector fields with suitable modulus of continuity
• An Overview on Some Results Concerning the Transport Equation and its Applications to Conservation Laws
• Mass transport in multicomponent compressible fluids: Local and global\n well-posedness in classes of strong solutions for general class-one models
• Local well-posedness in the Wasserstein space for a chemotaxis model coupled to Navier-Stokes equations