Guido Cavallaro, Roberto Garra and Carlo Marchioro
Localization and stability of active scalar flows
Received: 13 March 2013
Accepted: 16 April 2013
Mathematics Subject Classification (2010): 76B47, 76E20, 86A99.
Keywords: Quasigeostrophic flow, localization, stability.
Abstract: In this paper we discuss the time evolution of a two-dimensional active scalar flow. We extend to this dynamical system some rigorous results valid for a two-dimensional incompressible nonviscous fluid. In particular we study some characteristics of the dynamics when the initial field is concentrated in N small disjoint regions and we discuss the generalization of the localization. We investigate also the vanishing viscosity limit. Moreover we give some results of stability for the active scalar flow.