44 citations · 145 across the 27 of their papers we have counts for
19 papers · 1 filter
Semilinear Neumann boundary value problems for measure-valued maps
Aleksei Kroshnin, Hugo Lavenant, Dmitry Vorotnikov
We study the Wasserstein lift of nonlinear Poisson systems with inhomogeneous Neumann boundary conditions. We establish the existence of minimizers using new estimates involving th…
A unified duality framework for barotropic, quantum and Korteweg fluids
Dmitry Vorotnikov
We investigate a dual variational formulation, in the spirit of Brenier, for several compressible fluid models: the compressible barotropic Euler system, the quantum Euler system,…
On the variational dual formulation of the Nash system and an adaptive convex gradient-flow approach to nonlinear PDEs
Dmitry Vorotnikov, Amit Acharya
We investigate the influence of base states on the consistency of the dual variational formulation for quadratic systems of PDEs, which are not necessarily conservative (typical ex…
Dafermos' principle and Brenier's duality scheme for defocusing dispersive equations
Dmitry Vorotnikov
We discover an abstract structure behind several nonlinear dispersive equations (including the NLS, NLKG and GKdV equations with generic defocusing power-law nonlinearities) that i…
Overdamped Dynamics of a Falling Inextensible Network: Existence of Solutions
Ayk Telciyan, Dmitry Vorotnikov
We study the equations of overdamped motion of an inextensible triod with three fixed ends and a free junction under the action of gravity. The problem can be expressed as a system…
Uniformly compressing mean curvature flow
Wenhui Shi, Dmitry Vorotnikov
Michor and Mumford showed that the mean curvature flow is a gradient flow on a Riemannian structure with a degenerate geodesic distance. It is also known to destroy the uniform den…