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Global nonlinear stability for steady ideal fluid flow in bounded planar domains. (English) Zbl 1064.76053
Summary: We prove stability of steady flows of an ideal fluid in a bounded, simply connected, planar region, that are strict maximisers or minimisers of kinetic energy on an isovortical surface. The proof uses conservation of energy and transport of vorticity for solutions of the vorticity equation with initial data in $$L^{p}$$ for $$p > 4/3$$. A related stability theorem using conservation of angular momentum in a circular domain is also proved.

##### MSC:
 76E30 Nonlinear effects in hydrodynamic stability 35Q35 PDEs in connection with fluid mechanics
##### Keywords:
erngy minimizer; conservation of energy; vorticity equation
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##### References:
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