Concept

Théorème de Helmholtz-Hodge

Publications associées (39)

Anomalous dissipation and other non-smooth phenomena in fluids

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

EPFL2024

ALMOST EVERYWHERE NONUNIQUENESS OF INTEGRAL CURVES FOR DIVERGENCE-FREE SOBOLEV VECTOR FIELDS

Massimo Sorella

We construct divergence-free Sobolev vector fields in C([0,1];W-1,W-r(T-d;Rd)) with r < d and d\geq 2 which simultaneously admit any finite number of distinct positive solutions to the continuity equation. These vector fields are then shown to have at leas ...

Philadelphia2023

On the commutativity of flows of rough vector fields

Maria Colombo, Riccardo Tione

In the class of Sobolev vector fields in R-n of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commutes in terms of the Lie bracket and of a regularity cond ...

ELSEVIER2022

Homogenization of Multiscale Eddy Current Problem by Localized Orthogonal Decomposition Method

Xiaotao Ren

A homogenization approach for the solution of multiscale eddy current problem is proposed. The method is based on the subspace decomposition and it involves a coarse space and a nested fine space. The homogenized problem is posed in the coarse space with t ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2019

Helical equilibrium magnetohydrodynamic flow effects on the stability properties of low-n ideal external-infernal modes in weak shear tokamak configurations

Jonathan Graves, Wilfred Anthony Cooper, Daniele Brunetti, Alberto Mariani

The impact of equilibrium helical flows on the stability properties of low shear tokamak plasmas is assessed. The corrections due to such helical flow to the equilibrium profiles (mass density, pressure, Shafranov shift, magnetic fluxes) are computed by mi ...

IOP PUBLISHING LTD2019

LTCC magnetic sensors at EPFL and TCV: Lessons learnt for ITER

Duccio Testa, Xavier Llobet, Matthieu Toussaint, Pierre Lavanchy, Ugo Siravo, Frédéric Dolizy, Steve Couturier, Severino Antonioni, Christian Moura, Jonathan Bryan Lister, Thomas Maeder, Philippe Marmillod, Caroline Jacq, Blaise Marlétaz, Aylwin Iantchenko, Lorenzo Stipani, Adrien Aymeric Thibault Corne, Matthias Garcin

Innovative 3D high-frequency magnetic sensors have been designed and manufactured in-house for installation on the Tokamak a Configuration Variable (TCV), and are currently routinely operational. These sensors combine the Low Temperature Co-fired Ceramic ( ...

2019

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Fabio Nobile, Francesca Bonizzoni

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

A Class Of Large Global Solutions For The Wave-Map Equation

Joachim Krieger, Elisabetta Chiodaroli

In this paper we consider the equation for equivariant wave maps from R3+1 to S-3 and we prove global in forward time existence of certain C-infinity-smooth solutions which have infinite critical Sobolev norm (H) overdot(3/4) (R-3) x (H) overdot(1/2) (R-3) ...

2017

Scrape-off-layer current loops and floating potential in limited tokamak plasmas

Paolo Ricci, Joaquim Loizu Cisquella, Paola Paruta, Federico David Halpern

We investigate the question of how plasma currents circulate and close in the scrape-off-layer (SOL) of convection-limited tokamak plasmas. A simplified two-fluid model describes how currents must evacuate charge at the sheaths due to cross-field currents ...

Cambridge University Press2017

Limiting absorption principle and well-posedness for the Helmholtz equation with sign changing coefficients

Hoài-Minh Nguyên

In this paper, we investigate the limiting absorption principle associated to and the well-posedness of the Helmholtz equations with sign changing coefficients which are used to model negative index materials. Using the reflecting technique introduced in [ ...

Elsevier2016

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Convergence analysis of Padé approximations for Helmholtz frequency response problems

Fabio Nobile, Francesca Bonizzoni

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018