Local recovery of a solenoidal vector field by an extension of the thin-plate spline technique

1993 ◽  
Vol 5 (2) ◽  
pp. 121-129 ◽  
Author(s):  
David Handscomb
Keyword(s):  
Vector Field ◽  
Thin Plate ◽  
Thin Plate Spline ◽  
Solenoidal Vector ◽  
Local Recovery ◽  
Solenoidal Vector Field

Magnetfeldbeschreibung mit verallgemeinerten poloidalen und toroidalen Skalaren

1972 ◽  
Vol 27 (8-9) ◽  
pp. 1167-1172 ◽  
Author(s):  
Gerhard Gerlich
Keyword(s):  
Vector Field ◽  
Magnetic Fields ◽  
Vector Fields ◽  
Solenoidal Vector ◽  
Integrability Conditions ◽  
Solenoidal Vector Field ◽  
Complicated Geometry

Abstract Representation of Magnetic Fields by Generalized poloidal and Toroidal Scalars Every solenoidal vector field can be represented by unique poloidal and toroidal scalars. This description is especially appropriate to the geometry of a sphere. A generalization which can be applied to a more or less complicated geometry could be elaborated by means of transforming integrability conditions of space into integrability conditions of surfaces. This formalism enables us to give simple proofs of other important representations of vector fields by two scalars (magnetic coordinates, complex-lamellar fields).

Global regularity for a model Navier–Stokes equations on ℝ3

Analysis ◽  
2015 ◽  
Vol 35 (3) ◽  
Author(s):  
Dongho Chae
Keyword(s):  
Vector Field ◽  
Global Regularity ◽  
Stokes Equations ◽  
Time Dependent ◽  
Navier Stokes ◽  
Nonlinear Parabolic System ◽  
Solenoidal Vector ◽  
Navier Stokes Equations ◽  
Nonlinear Parabolic ◽  
Solenoidal Vector Field

AbstractWe study a nonlinear parabolic system for a time dependent solenoidal vector field on ℝ

scholarly journals Thin-plate-Spline Curvilinear Meshing on a Calculus-of-Variations Framework

2015 ◽  
Vol 124 ◽  
pp. 135-147 ◽  
Author(s):  
Shankar P. Sastry ◽  
Vidhi Zala ◽  
Robert M. Kirby
Keyword(s):  
Calculus Of Variations ◽  
Thin Plate ◽  
Thin Plate Spline
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