相关论文: Flow Equations for Hamiltonians from Continuous Un…

We establish kinetic Hamiltonian flows in density space embedded with the $L^2$-Wasserstein metric tensor. We derive the Euler-Lagrange equation in density space, which introduces the associated Hamiltonian flows. We demonstrate that many…

We derive renormalised finite functional flow equations for quantum field theories in real and imaginary time that incorporate scale transformations of the renormalisation conditions, hence implementing a flowing renormalisation. The flows…

We provide a method to select flows of solutions to the Cauchy problem for linear and nonlinear Fokker--Planck--Kolmogorov equations (FPK equations) for measures on Euclidean space. In the linear case, our method improves similar results of…

We study Hamiltonian flows in a real separable Hilbert space endowed with a symplectic structure. Measures on the Hilbert space that are invariant with respect to the flows of completely integrable Hamiltonian systems are investigated.…

The celebrated Antezana-Pujals-Stojanoff Theorem states that the iterated Aluthge transforms of an arbitrary matrix converge to a normal matrix. We introduce a family of matrix flows that share this convergence property by defining them…

In this paper, we study the dynamical aspects of the \emph{Hamiltonian homeomorphism group} $Hameo(M,\omega)$ which was introduced by M\"uller and the author. We introduce the notion of autonomous continuous Hamiltonian flows and extend the…

The paper reports the recent results on application and extension of the matrix formulation of lagrangian hydrodynamic equations. The matrix approach is based on the notion of continuous deformation of infinitesimal material elements and…

The Fokker-Planck equation is one of the fundamental equations in nonequilibrium statistical mechanics, and this equation is known to be derived from the Wasserstein gradient flow equation with a free energy. This gradient flow equation…

This work is the second part of a program initiated in arXiv:2111.13258 aiming at the development of an intrinsic geometric well-posedness theory for Hamilton-Jacobi equations related to controlled gradient flow problems in metric spaces.…

A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…

This paper gives a new unified formula for the Newtonian fluids valid for all pipe flow regimes from laminar to the fully rough turbulent. It includes laminar, unstable sharp jump from laminar to turbulent, and all types of the turbulent…

We complement a recent work on the stability of fixed points of the CMC-Einstein-$\Lambda$ flow. In particular, we modify the utilized gauge for the Einstein equations and remove a restriction on the fixed points whose stability we are able…

We develop a Hamiltonian theory for 2D soliton equations. In particular, we identify the spaces of doubly periodic operators on which a full hierarchy of commuting flows can be introduced, and show that these flows are Hamiltonian with…

In this paper we consider the problem of obtaining a general port-Hamiltonian formulation of Newtonian fluids. We propose the port-Hamiltonian models to describe the energy flux of rotational three-dimensional isentropic and non-isentropic…

Flows on the moduli space of the algebraic Riemann surfaces, preserving the periods of the corresponding solutions of the soliton equations are studied. We show that these flows are gradient with respect to some indefinite symmetric flat…

We give an application of a Huisken monotonicity-type formula for the mean curvature flow in a compact smooth manifold with a Riemannian metric that evolves by a shrinking self-similar solution of the extended Ricci flow. Our investigation…

The theory of integrable systems of Hamiltonian PDEs and their near-integrable deformations is used to study evolution equations resulting from vertical-averages of the Euler system for two-layer stratified flows in an infinite 2D channel.…

The notion of the flow introduced by Kitaev is a manifestly topological formulation of the winding number on a real lattice. First, we show in this paper that the flow is quite useful for practical numerical computations for systems without…

We consider flow-structure interactions modeled by a modified wave equation coupled at an interface with equations of nonlinear elasticity. Both subsonic and supersonic flow velocities are treated with Neumann type flow conditions, and a…

In this paper, we introduce a class of new logarithmic curvature flow. The flows are designed to embrace the monotonicity of the related functional, and the convergence of this flow would tackle the solvability of the weighted…