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Some Stability and Instability Criteria for Ideal Plane Flows

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Abstract

We investigate stability and instability of steady ideal plane flows for an arbitrary bounded domain. First, we obtain some general criteria for linear and nonlinear stability. Second, we find a sufficient condition for the existence of a growing mode to the linearized equation. Third, we construct a steady flow which is nonlinearly and linearly stable in the L 2 norm of vorticity but linearly unstable in the L 2 norm of velocity.

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  1. Department of Mathematics, Brown University, Providence, RI 02912, USA

    Zhiwu Lin

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  1. Zhiwu Lin
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Communicated by P. Constantin

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Lin, Z. Some Stability and Instability Criteria for Ideal Plane Flows. Commun. Math. Phys. 246, 87–112 (2004). https://doi.org/10.1007/s00220-004-1045-3

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  • DOI: https://doi.org/10.1007/s00220-004-1045-3

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