Abstract.
Incompressible perfect fluids are described by the Euler equations. We provide a new simple proof for well-posedness for velocities in \(C^{1,\alpha}\) and linear and nonlinear instability results using transport techniques. The results have an important consequence: the topology of \(C^{1,\alpha}\) is too fine for interesting questions about large time behavior.
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Received: 14 September 2001 / Published online: 4 April 2002
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Koch, H. Transport and instability for perfect fluids. Math Ann 323, 491–523 (2002). https://doi.org/10.1007/s002080200312
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DOI: https://doi.org/10.1007/s002080200312