Variational methods, multisymplectic geometry and continuum mechanics

Abstract

This paper presents a variational and multisymplectic formulation of both compressible and incompressible models of continuum mechanics on general Riemannian manifolds. A general formalism is developed for non-relativistic first-order multisymplectic field theories with constraints, such as the incompressibility constraint. The results obtained in this paper set the stage for multisymplectic reduction and for the further development of Veselov-type multisymplectic discretizations and numerical algorithms. The latter will be the subject of a companion paper.

References in corpus (4)

• Multisymplectic geometry, variational integrators, and nonlinear PDEs
• Multisymplectic geometry, covariant Hamiltonians, and water waves
• Second-order multisymplectic field theory: A variational approach to second-order multisymplectic field theory
• Geometry and curvature of diffeomorphism groups with $H^1$ metric and mean hydrodynamics

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• On Higher Derivatives as Constraints in Field Theory: a Geometric Perspective
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