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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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