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

Albert Clop, Heikki Jylhä, Joan Orobitg, Juan Eugenio Mateu Bennassar

Research output: Contribution to journalArticleResearch

1 Citation (Scopus)

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, H-1, for the scalar conservation law induced by a class of vector fields whose divergence is an unbounded BMO function. (C) 2018 Elsevier Inc. All rights reserved.

Original languageEnglish
Pages (from-to)45-77
Number of pages33
JournalJournal of Functional Analysis
Volume276
Issue number1
DOIs
Publication statusPublished - 1 Jan 2019

Keywords

  • Continuity equation
  • EULER EQUATIONS
  • Hardy space
  • Mass transport
  • ORDINARY DIFFERENTIAL-EQUATIONS
  • TRANSPORT-EQUATION
  • UNIQUENESS

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