On the flow map for 2D Euler equations with unbounded vorticity

Details On the flow map for 2D Euler equations with unbounded vorticity On the flow map for 2D Euler equations with unbounded vorticity

2011-08-10

arxiv.org/abs/1108.2079v1

Nonlinearity 24 (2011) 2599-2637

Mathematics

Analysis of PDEs

http://iopscience.iop.org/0951-7715/24/9/013/ for published version

Scientific paper

In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map.

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