Nonlinear Stability of Vortex Patches

Yun Tang
1987 Transactions of the American Mathematical Society  
To establish the nonlinear (Liapunov) stability of both circular and elliptical vortex patches in the plane for the nonlinear dynamical system generated by the two-dimensional Euler equations of incompressible, inviscid hydrodynamics. This is accomplished by using a relative variational principle in terms of energy function. A counterexample shows that our result in the case of an elliptical vortex patch is the best one that can be attained by applying the energy estimate.
doi:10.2307/2000733 fatcat:si7tafgwfjgltdt3hx5ojux6dy