Nonlinear Stability of Rotating Patterns

Beyn W-J, Lorenz J (2008)
Dynamics of Partial Differential Equations 5(4): 349-400.

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
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Abstract / Bemerkung
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.
Erscheinungsjahr
Zeitschriftentitel
Dynamics of Partial Differential Equations
Band
5
Ausgabe
4
Seite(n)
349-400
ISSN
PUB-ID

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Beyn W-J, Lorenz J. Nonlinear Stability of Rotating Patterns. Dynamics of Partial Differential Equations. 2008;5(4):349-400.
Beyn, W. - J., & Lorenz, J. (2008). Nonlinear Stability of Rotating Patterns. Dynamics of Partial Differential Equations, 5(4), 349-400. doi:10.4310/DPDE.2008.v5.n4.a4
Beyn, W. - J., and Lorenz, J. (2008). Nonlinear Stability of Rotating Patterns. Dynamics of Partial Differential Equations 5, 349-400.
Beyn, W.-J., & Lorenz, J., 2008. Nonlinear Stability of Rotating Patterns. Dynamics of Partial Differential Equations, 5(4), p 349-400.
W.-J. Beyn and J. Lorenz, “Nonlinear Stability of Rotating Patterns”, Dynamics of Partial Differential Equations, vol. 5, 2008, pp. 349-400.
Beyn, W.-J., Lorenz, J.: Nonlinear Stability of Rotating Patterns. Dynamics of Partial Differential Equations. 5, 349-400 (2008).
Beyn, Wolf-Jürgen, and Lorenz, Jens. “Nonlinear Stability of Rotating Patterns”. Dynamics of Partial Differential Equations 5.4 (2008): 349-400.