Publication
On a Lagrangian Formulation of the Incompressible Euler Equation
Related publications (37)
From low-rank retractions to dynamical low-rank approximation and back
Daniel Kressner, Axel Elie Joseph Séguin, Gianluca Ceruti
In algorithms for solving optimization problems constrained to a smooth manifold, retractions are a well-established tool to ensure that the iterates stay on the manifold. More recently, it has been demonstrated that retractions are a useful concept for ot ...
Springer2024Retraction-based numerical methods for continuation, interpolation and time integration on manifolds
The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...
EPFL2023A b-symplectic slice theorem
In this article, motivated by the study of symplectic structures on manifolds with boundary and the systematic study of b-symplectic manifolds started in Guillemin, Miranda, and Pires Adv. Math. 264 (2014), 864-896, we prove a slice theorem for Lie group a ...
WILEY2022Dynamical Reduced Basis Methods for Hamiltonian Systems
We consider model order reduction of parameterized Hamiltonian systems describing nondissipative phenomena, like wave-type and transport dominated problems. The development of reduced basis methods for such models is challenged by two main factors: the ric ...
2019On the Lagrangian structure of transport equations: The Vlasov–Poisson system
The Vlasov-Poisson system is an important nonlinear transport equation, used to describe the evolution of particles under their self-consistent electric or gravitational field. The existence of classical solutions is limited to dimensions d
2017Dynamical Low Rank approximation of PDEs with random parameters
In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...
EPFL2017The tropical momentum map: a classification of toric log symplectic manifolds
We give a generalization of toric symplectic geometry to Poisson manifolds which are symplectic away from a collection of hypersurfaces forming a normal crossing configuration. We introduce the tropical momentum map, which takes values in a generalization ...
Springer Verlag2017Eigenfunction Expansions Of Ultradifferentiable Functions And Ultradistributions
In this paper we give a global characterisation of classes of ultradifferentiable functions and corresponding ultradistributions on a compact manifold X. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on X. Th ...
American Mathematical Society2016Eigenfunction expansions of ultradifferentiable functions and ultradistributions
In this paper we give a global characterisation of classes of ultradi_erentiable functions and corresponding ultradistributions on a compact manifold X. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on X. Thi ...
2016On the well-posedness of the Holm-Staley b-family of equations
In this paper we consider the Holm-Staley b-family of equations in the Sobolev spaces H-s (R) for s > 3/2. Using a geometric approach we show that, for any value of the parameter b, the corresponding solution map, u(0) bar right arrow u(T), is nowhere loca ...
Taylor & Francis Ltd2016