A unified treatment of ODEs under Osgood and Sobolev type conditions

Details A unified treatment of ODEs under Osgood and Sobolev type conditions A unified treatment of ODEs under Osgood and Sobolev type conditions

2011-07-13

arxiv.org/abs/1107.2496v1

Mathematics

Classical Analysis and ODEs

14 pages

Scientific paper

In this paper we prove the existence, uniqueness and regularity of the
DiPerna--Lions flow generated by a vector field which is "almost everywhere
Osgood continuous", following Crippa and de Lellis's direct method. As an
application, we show the well-posedness of transport equations in the space of
nonnegative integrable functions.

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