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 : https://apps.dtic.mil/dtic/tr/fulltext/u2/1024234.pdf


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