Representation of vector fields

 
 
 
  • Abstract
  • Keywords
  • References
  • PDF
  • Abstract


    A simple proof is given for the explicit formula which allows one to recover a \(C^2\) – smooth vector field \(A=A(x)\) in \(\mathbb{R}^3\), decaying at infinity, from the knowledge of its \(\nabla \times A\) and \(\nabla \cdot A\). The representation of \(A\) as a sum of the gradient field and a divergence-free vector fields is derived from this formula. Similar results are obtained for a vector field in a bounded \(C^2\) - smooth domain.


  • Keywords


    Vector elds; Representation of vector elds.

  • References


      [1] O. Ladyzhenskaya, The mathematical theory of viscous incompressible fluid, Gordon and Breach, New York, 1969.

      [2] D. Menzel, Fundamental formulas of physics, Prentice Hall, New York, 1955.

      [3] R. Temam, Navier-Stokes equations, North Holland, Amsterdam, 1984.


 

View

Download

Article ID: 4577
 
DOI: 10.14419/gjma.v3i2.4577




Copyright © 2012-2015 Science Publishing Corporation Inc. All rights reserved.