Riv. Mat. Univ. Parma, Vol. 4, No. 1, 2013

Guido Cavallaro, Roberto Garra and Carlo Marchioro

Localization and stability of active scalar flows

Pages: 175-196
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.

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