Well-posedness for the continuity equation for vector fields with suitable modulus of continuity

2017/01/17 by Albert Clop, Heikki Jylhä, Clop, Albert +5
Mathematics · #35F10 #35L65 #35R05 #37C10 #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #math.AP #math.CA #msc:35F10 #msc:35L65 #msc:35R05 #msc:37C10

paper · pdf · doi:10.48550/arxiv.1701.04603

arxiv created 2017/01/17 · arxiv updated 2017/01/18

Abstract

We prove well-posedness of linear scalar conservation laws using only assumptions on the growth and the modulus of continuity of the velocity field, but not on its divergence. As an application, we obtain uniqueness of solutions in the atomic Hardy space, H1, for the scalar conservation law induced by a class of vector fields whose divergence is an unbounded BMO function.

Related

• Some new well-posedness results for continuity and transport equations, and applications to the chromatography system
• On the one-dimensional continuity equation with a nearly incompressible vector field
• Scalar conservation laws with discontinuous flux: existence and uniqueness
• An Overview on Some Results Concerning the Transport Equation and its Applications to Conservation Laws
• Well-posedness for conservation laws with spatial heterogeneities and a study of BV regularity