Eulerian Dynamics with a Commutator Forcing
University of Illinois Chicago United States
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We study a general class of Euler equations driven by a forcing with a commutator structure of the form L, up Lpu-Lpu, where u is the velocity field and L is the action which belongs to a rather general class of translation invariant operators. Such systems arise, for example, as the hydrodynamic description of velocity alignment, where action involves convolutions with bounded, positive influence kernels, Lphif phi f. Our interest lies with a much larger class of Ls which are neither bounded nor positive. In this paper we develop a global regularity theory in the one-dimensional setting, considering three prototypical sub-classes of actions.
- Numerical Mathematics