We study completeness properties of the Sobolev diffeomorphism groups Ds (M) endowed
with strong right-invariant Riemannian metrics when M is Rd or a compact manifold without …

We study properties of Sobolev-type metrics on the space of immersed plane curves. We
show that the geodesic equation for Sobolev-type metrics with constant coefficients of order …

In this paper, we derive a two-component system of nonlinear equations which models two-
dimensional shallow water waves with constant vorticity. Then, we prove well-posedness of …

Rational solutions of the inhomogeneous Painlevé-II equation and of a related coupled
Painlevé-II system have recently arisen in studies of fluid vortices and of the sine-Gordon …

In this paper, we study the geodesic flow of a right-invariant metric induced by a general
Fourier multiplier on the diffeomorphism group of the circle and on some of its homogeneous …

This article consists of a detailed geometric study of the one-dimensional vorticity model
equation ω t+ u ω x+ 2 ω ux= 0, ω= H ux, t∈ R, x∈ S 1, which is a particular case of the …

Of concern is the study of fractional order Sobolev-type metrics on the group of H∞-
diffeomorphism of R d and on its Sobolev completions D q (R d). It is shown that the H s …

This article is concerned with the mathematical analysis of the perturbation method for
extended Kohn–Sham models, in which fractional occupation numbers are allowed. All our …

The subject of so-called objective derivatives in Continuum Mechanics has a long history
and has generated varying views concerning their true mathematical interpretation. Several …

Many models in mathematical physics are given as non-linear partial differential equation of
hydrodynamic type; the incompressible Euler, KdV, and Camassa–Holm equations are well …