A theorem on measures in dimension 2 and applications to vortex sheets

2013/10/10 by Tomasz Cieslak, Cieslak, Tomasz, Marta Szumanska +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #math.AP #math.FA

paper · pdf · doi:10.48550/arxiv.1310.2666

arxiv created 2013/10/10 · arxiv updated 2013/10/11

Abstract

We find conditions under which measures belong to . Next we show that measures generated by Prandtl, Kaden as well as Pullin spirals, objects considered by physicists as incompressible flows generating vorticity, satisfy assumptions of our theorem, thus they are (locally) elements of . Moreover, as a by-product, we prove an embedding of the space of Morrey type measures in .

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