Related papers: Using Euler-Lagrange Variational Principle to Obta…
We prove a novel stability estimate in $L^\infty _t (L^p _x)$ between the regular Lagrangian flow of a Sobolev vector field and a piecewise affine approximation of such flow. This approximation of the flow is obtained by a (sort of)…
This paper is concerned with analyzing a class of fractional calculus of variations problems and their associated Euler-Lagrange (fractional differential) equations. Unlike the existing fractional calculus of variations which is based on…
In this note we consider general formulation of Euler's equations for an inviscid incompressible homogeneous fluid with an oscillating body force. Our aim is to derive the averaged equations for these flows with the help of two-timing…
The pressure in a classical Coulomb fluid at equilibrium is obtained from the Maxwell tensor at some point inside the fluid, by a suitable statistical average. For fluids in an Euclidean space, this is a fresh look on known results. But,…
Fluids can behave in a highly irregular, turbulent way. It has long been realised that, therefore, some weak notion of solution is required when studying the fundamental partial differential equations of fluid dynamics, such as the…
Single component nonrelativistic dissipative fluids are treated independently of reference frames and flow-frames. First the basic fields and their balances, then the related thermodynamic relations and the entropy production are calculated…
A new Hamiltonian formulation for the fully nonlinear water-wave problem over variable bathymetry is derived, using an exact, vertical series expansion of the velocity potential, in conjunction with Luke's variational principle. The…
A flow vessel with an elastic wall can deform significantly due to viscous fluid flow within it, even at vanishing Reynolds number (no fluid inertia). Deformation leads to an enhancement of throughput due to the change in cross-sectional…
The Lagrangian formulation for the irrotational wave motion is straightforward and follows from a Lagrangian functional which is the difference between the kinetic and the potential energy of the system. In the case of fluid with constant…
In this article we consider the inhomogeneous incompressible Euler equations describing two fluids with different constant densities under the influence of gravity as a differential inclusion. By considering the relaxation of the…
The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations. The studied equations are considered in Lagrangian description, making it possible to find a Lagrangian such that the relativistic gas…
We investigate by direct numerical simulations the flow that rising bubbles cause in an originally quiescent fluid. We employ the Eulerian-Lagrangian method with two-way coupling and periodic boundary conditions. In order to be able to…
Following the idea that dissipation in turbulence at high Reynolds number is by events singular in space-time and described by solutions of the inviscid Euler equations, we draw the conclusion that in such flows scaling laws should depend…
We review some recent developments in mathematical aspects of relativistic fluids. The goal is to provide a quick entry point to some research topics of current interest that is accessible to graduate students and researchers from adjacent…
We present here a constructive method of Lagrangian approximate control- lability for the Euler equation. We emphasize on different options that could be used for numerical recipes: either, in the case of a bi-dimensionnal fluid, the use of…
We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the…
The present paper is an attempt to demonstrate how the energy minimization principle may be considered as a governing rule for the physical equilibrium that determines the flow fields in tubes and networks. We previously investigated this…
This is an annotated translation from Latin of 'Principia pro motu sanguinis per arterias determinando' in which Euler develops the first known work on the mechanics of flows in elastic tubes, intended to the first contest of the Dijon…
We consider solutions to the two-dimensional incompressible Euler system with only integrable vorticity, thus with possibly locally infinite energy. With such regularity, we use the recently developed theory of Lagrangian flows associated…
We show how dynamical equations for liquid films and drops on uneven surfaces, including contact line dynamics and evaporation/condensation effects, may be formulated as a variational dynamics, generated via Onsager's variational principle.…