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Person# Boris Buffoni

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Derivative

In mathematics, the derivative shows the sensitivity of change of a function's output with respect to the input. Derivatives are a fundamental tool of calculus. For example, the derivative of the p

Stream function

The stream function is defined for incompressible (divergence-free) flows in two dimensions – as well as in three dimensions with axisymmetry. The flow velocity components can be expressed as the der

Surface tension

Surface tension is the tendency of liquid surfaces at rest to shrink into the minimum surface area possible. Surface tension is what allows objects with a higher density than water such as razor b

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Courses taught by this person (4)

MATH-106(a): Analysis II

Étudier les concepts fondamentaux d'analyse, et le calcul différentiel et intégral des fonctions réelles de plusieurs
variables.

MATH-106(f): Analysis II

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles de plusieurs
variables.

MATH-302: Functional analysis I

Concepts de base de l'analyse fonctionnelle linéaire: opérateurs bornés, opérateurs compacts, théorie spectrale pour les opérateurs symétriques et compacts, le théorème de Hahn-Banach, les théorèmes de l'application ouverte et du graphe fermé.

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Using a variational method, we prove the existence of heteroclinic solutions for a 6-dimensional system of ordinary differential equations. We derive this system from the classical Benard-Rayleigh problem near the convective instability threshold. The constructed heteroclinic solutions provide first order approximations for domain walls between two orthogonal convective rolls.(c) 2023 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).

Fully localised three-dimensional solitary waves are steady water waves which are evanescent in every horizontal direction. Existence theories for fully localised three-dimensional solitary waves on water of finite depth have recently been published, and in this paper we establish their existence on deep water. The governing equations are reduced to a perturbation of the two-dimensional nonlinear Schrodinger equation, which admits a family of localised solutions. Two of these solutions are symmetric in both horizontal directions and an application of a suitable variant of the implicit-function theorem shows that they persist under perturbations.

We consider the stationary flow of an inviscid and incompressible fluid of constant density in the region D = (0, L) x R-2. We are concerned with flows that are periodic in the second and third variables and that have prescribed flux through each point of the boundary aD. The Bernoulli equation states that the "Bernoulli function" H :=-1/2 vertical bar v vertical bar(2) + p (where v is the velocity field and p the pressure) is constant along stream lines, that is, each particle is associated with a particular value of H. We also prescribe the value of H on partial derivative D. The aim of this work is to develop an existence theory near a given constant solution. It relies on writing the velocity field in the form v = del f x del g and deriving a degenerate nonlinear elliptic system for f and g. This system is solved using the Nash Moser method, as developed for the problem of isometric embeddings of Riemannian manifolds; see, e.g., the book by Q. Han and J.-X. Hong (2006). Since we can allow H to be nonconstant on partial derivative D, our theory includes three-dimensional flows with nonvanishing vorticity.