Accession Number : AD1024234

Title :   Eulerian Dynamics with a Commutator Forcing

Descriptive Note : Technical Report

Corporate Author : University of Illinois Chicago United States

Personal Author(s) : Shvydkoy,Roman ; Tadmor,Eitan

Full Text :

Report Date : 09 Jan 2017

Pagination or Media Count : 22

Abstract : We study a general class of Euler equations driven by a forcing with a commutator structure of the form [L, u](p) = L(pu)-L(p)u, 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, Lphi(f) = phi * f. Our interest lies with a much larger class of L's 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.

Descriptors :   partial differential equations , navier stokes equations , commutators , euler equations

Subject Categories : Numerical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE