The authors investigate the stability of a steady ideal plane flow in an arbitrary domain in terms of the L^2 norm of the vorticity. Linear stability implies nonlinear instability provided the growth rate of the line...The authors investigate the stability of a steady ideal plane flow in an arbitrary domain in terms of the L^2 norm of the vorticity. Linear stability implies nonlinear instability provided the growth rate of the linearized system exceeds the Liapunov exponent of the flow. In contrast,a maximizer of the entropy subject to constant energy and mass is stable. This implies the stability of certain solutions of the mean field equation.展开更多
文摘The authors investigate the stability of a steady ideal plane flow in an arbitrary domain in terms of the L^2 norm of the vorticity. Linear stability implies nonlinear instability provided the growth rate of the linearized system exceeds the Liapunov exponent of the flow. In contrast,a maximizer of the entropy subject to constant energy and mass is stable. This implies the stability of certain solutions of the mean field equation.
