Related papers: A Gauge-Theoretic Action Principle for Viscous Inc…
This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous…
We introduce a new approach to Monge-Ampere geometry based on techniques from higher symplectic geometry. Our work is motivated by the application of Monge-Ampere geometry to the Poisson equation for the pressure that arises for…
Hamilton's principle plays a central role in fluid mechanics as a fundamental tool for deriving governing equations, analyzing conservation laws, and designing structure-preserving numerical schemes. However, its classical formulation is…
The coupling between dilatation and vorticity, two coexisting and fundamental processes in fluid dynamics is investigated here, in the simplest cases of inviscid 2D isotropic Burgers and pressureless Euler-Coriolis fluids respectively…
In this paper, we consider an incompressible viscous flow without surface tension in a finite-depth domain of three dimensions, with free top boundary and fixed bottom boundary. This system is governed by a Naiver-Stokes equation in above…
The purpose of this paper is to derive rigorously the so called viscous shallow water equations given for instance page 958-959 in [A. Oron, S.H. Davis, S.G. Bankoff, Rev. Mod. Phys, 69 (1997), 931?980]. Such a system of equations is…
This paper investigates the dynamics of time-periodic Euler flows in multi-connected, planar fluid regions which are ``stirred'' by the moving boundaries. The classical Helmholtz theorem on the transport of vorticity implies that if the…
In ideal fluids, Clebsch potentials occur as paired canonical variables associated with the Hamiltonian description of the Euler equations. This paper explores the properties of the incompressible Navier-Stokes equations when the velocity…
The incompressible Navier-Stokes (NS) equation is known to govern the hydrodynamic limit of essentially any fluid and its rich non-linear structure has critical implications in both mathematics and physics. The employability of the methods…
With the goal of deriving dissipative hydrodynamics from an action, we study classical actions for open systems, which follow from the generic structure of effective actions in the Schwinger-Keldysh Closed-Time-Path formalism with two time…
We consider the inviscid limit for the two-dimensional incompressible Navier-Stokes equation in the particular case where the initial flow is a finite collection of point vortices. We suppose that the initial positions and the circulations…
The two-dimensional Navier-Stokes equations are rewritten as a system of coupled nonlinear ordinary differential equations. These equations describe the evolution of the moments of an expansion of the vorticity with respect to Hermite…
We present a novel multi-fluid model for compressible two-phase flows. The model is derived through a newly developed Stationary Action Principle framework. It is fully closed and introduces a new interfacial quantity, the interfacial work.…
As a model for vortex-wall interactions, we consider the two-dimensional incompressible Navier--Stokes equations in the half-plane $R^2_+$ with no-slip boundary condition and point vortices as initial data. We focus on the paradigmatic…
We investigate the two dimensional incompressible Navier-Stokes(NS) and the continuity equations in Cartesian coordinates and Eulerian description for non-Newtonian fluids. As a non-Newtonian viscosity we consider the Ladyzenskaya model…
We show that the widely used model governing the motion of two incompressible immiscible fluids in a possibly heterogeneous porous medium has a formal gradient flow structure. More precisely, the fluid composition is governed by the…
We consider a new way of establishing Navier wall laws. Considering a bounded domain $\Omega$ of R N , N=2,3, surrounded by a thin layer $\Sigma \epsilon$, along a part $\Gamma$2 of its boundary $\partial \Omega$, we consider a…
A fluid described by an Abelian Chern-Simons action principle in 4+1 dimensions is considered. Letting 3+1 dimensions correspond to the usual space and time, and assuming the fields to be independent of the fifth coordinate, the free theory…
The derivation of shallow water models from Navier-Stokes equations is revisited yielding a class of two-layer shallow water models.An improved velocity profile is proposed, based on the superposition of an ideal fluid and a viscous layer…
We further develop a recently introduced variational principle of stationary action for problems in nonconservative classical mechanics and extend it to classical field theories. The variational calculus used is consistent with an initial…