Eulerian Dynamics with a Commutator Forcing

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.

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Document Details

Document Type
Technical Report
Publication Date
Jan 09, 2017
Accession Number
AD1024234

Entities

People

  • Eitan Tadmor
  • Roman Shvydkoy

Organizations

  • University of Illinois at Chicago

Tags

Communities of Interest

  • C4I
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Commutators
  • Computational Fluid Dynamics
  • Computational Science
  • Computer Science
  • Convolution
  • Differential Equations
  • Diffusion
  • Equations
  • Euler Equations
  • Formulas (Mathematics)
  • Inequalities
  • Integrals
  • Mathematics
  • Navier Stokes Equations
  • Partial Differential Equations
  • Riccati Equation

Fields of Study

  • Mathematics

Readers

  • Computational Fluid Dynamics (CFD)
  • Control Systems Engineering.
  • Linear Algebra