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28 p, 509.2 KB Well-posedness for the continuity equation for vector fields with suitable modulus of continuity / Clop, Albert (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Jylhä, Heikki (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Orobitg i Huguet, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques) ; Mateu Bennassar, Joan (Universitat Autònoma de Barcelona. Departament de Matemàtiques)
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.
2019 - 10.1016/j.jfa.2018.10.001
Journal of Functional Analysis, Vol. 276, Issue 1 (January 2019) , p. 45-77  
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