Nonlinear Stability of Rotating Patterns
Beyn, Wolf-Jürgen
Beyn
Wolf-Jürgen
Lorenz, Jens
Lorenz
Jens
We consider 2D localized rotating patterns which solve a parabolic system of PDEs on the spatial domain R-2. Under suitable assumptions, we prove nonlinear stability with asymptotic phase with respect to the norm in the Sobolev space H-2. The stability result is obtained by a combination of energy and resolvent estimates, after the dynamics is decomposed into an evolution within a three-dimensional group orbit and a transversal evolution towards the group orbit. The stability theorem is applied to the quintic-cubic Ginzburg-Landau equation and illustrated by numerical computations.
5
4
349-400
349-400
International Press of Boston
2008