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

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...

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Published in:	Nonlinearity 2011-09, Vol.24 (9), p.2599-2637
Main Author:	KELLIHER, James P
Format:	Article
Language:	English
Subjects:	Construction Continuity Euler equations Exact sciences and technology Exponents Global analysis, analysis on manifolds Inverse problems Mathematical analysis Mathematical methods in physics Mathematics Nonlinearity Numerical analysis Numerical analysis in abstract spaces Numerical analysis. Scientific computation Other topics in mathematical methods in physics Partial differential equations Physics Planes Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Two dimensional
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description	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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subjects	Construction Continuity Euler equations Exact sciences and technology Exponents Global analysis, analysis on manifolds Inverse problems Mathematical analysis Mathematical methods in physics Mathematics Nonlinearity Numerical analysis Numerical analysis in abstract spaces Numerical analysis. Scientific computation Other topics in mathematical methods in physics Partial differential equations Physics Planes Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Two dimensional
title	On the flow map for 2D Euler equations with unbounded vorticity
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