Long time localization of modified surface quasi-geostrophic equations

Abstract

We discuss the time evolution of a two-dimensional active scalar flow, which extends some properties valid for a two-dimensional incompressible nonviscous fluid. In particular we study some characteristics of the dynamics when the field is initially concentrated in $N$ small disjoint regions, and we discuss the conservation in time of this localization property. We discuss also how long this localization persists, showing that in some cases this happens for quite long times.

References in corpus (6)

• Global regularity for a modified critical dissipative quasi-geostrophic equation
• Inviscid models generalizing the 2D Euler and the surface quasi-geostrophic equations
• Interaction of vortices in viscous planar flows
• Collapse of generalized Euler and surface quasi-geostrophic point-vortices
• Long time evolution of concentrated Euler flows with planar symmetry
• Regularization by noise for the point vortex model of mSQG equations

Cited by in corpus (1)

• Hölder regularity for collapses of point vortices