ISSN:
1422-6952
Keywords:
Keywords. Lagrange functional, stationary points, C2 solutions of the Euler equation.
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
,
Physics
Notes:
Abstract. We show in detail in which sense the following two properties of a time dependent, C 2-smooth, divergence-free vector field v are equivalent:¶a) v satisfies the Euler equation of hydrodynamics (with some pressure function p)¶b) v is a stationary point of a suitable Lagrange functional.¶Important steps are the study of surjectivity properties of the derivative of the action functional, and the identification of vector fields orthogonal to the divergence-free fields as gradients, in the sense of classical differentiability. Thus, a foundation of the Euler equation from a variational principle is provided in a form which, to the author's knowledge, was not available so far.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/s000210050016
