Log-resolutions, derivations, and evolutions

Anti-selfdual Hamiltonians: Variational resolutions for Navier-Stokes and other nonlinear evolutions

The theory of anti-selfdual (ASD) Lagrangians developed in [8] allows a variational resolution for equations of the form Λu+Au+∂φ(u)+f = 0 where φ is a convex lower-semi-continuous function on a reflexive Banach space X, f ∈ X∗, A : D(A) ⊂ X → X∗ is a positive linear operator and where Λ : D(Λ) ⊂ X → X∗ is a non-linear operator that satisfies suitable continuity and anti-symmetry properties. AS...

Anti-Symmetric Hamiltonians (II): Variational resolutions for Navier-Stokes and other nonlinear evolutions

The nonlinear selfdual variational principle established in the first part of this paper [8] – though good enough to be readily applicable in many stationary nonlinear partial differential equations – did not however cover the case of nonlinear evolutions such as the Navier-Stokes equations. One of the reasons is the prohibitive coercivity condition that is not satisfied by the corresponding se...

Anti-symmetric Hamiltonians: Variational resolutions for Navier-Stokes and other nonlinear evolutions

The theory of anti-selfdual (ASD) Lagrangians –introduced in [7]– is developed further to allow for a variational resolution of non-linear PDEs of the form Λu+Au+ ∂φ(u)+ f = 0 where φ is a convex lower-semi-continuous function on a reflexive Banach space X , f ∈ X∗, A : D(A) ⊂ X → X∗ is a positive linear operator and where Λ :D(Λ)⊂X→X∗ is a non-linear operator that satisfies suitable continuity...

Anti-selfdual Lagrangians: Variational resolutions of non self-adjoint equations and dissipative evolutions

We develop the concept and the calculus of anti-selfdual (ASD) Lagrangians and their “potentials” which seem inherent to many partial differential equations and evolutionary systems. They are natural extensions of gradients of convex functions –hence of self-adjoint positive operators– which usually drive dissipative systems, but also provide representations for the superposition of such gradie...

Government And The Economic Evolutions