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Fourier Analysis For And Partial Differential Equations

"This project aims to develop the field of Harmonic Analysis, and more precisely to study problems at the interface between Fourier Analysis and PDEs (and also some Geometry). We are interested in two aspects of the Fourier Analy... see more

30/11/2020

CNRS

941K€

Project Budget: 941K€

Project leader

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

PARTICIPATION DEPralty Sin fecha límite de participación.

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Financing granted El organismo H2020 notifico la concesión del proyecto The day 2020-11-30

ERC-StG-2014: ERC Starting Grant Scope:Objectives

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Cerrada does 11 years

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2 Participantes

CNRS

940.54K€ | Leader

BERLYS CORPORACION ALIMENTAR...

391.48K€ | participant

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Project duration: 66 months Date Start: 2015-05-06
End date: 2020-11-30

Project leader

CENTRE NATIONAL DE LA RECHERCHE SCIENTIFIQUE... No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Project Budget 941K€

participation deadline Sin fecha límite de participación.

Project description "This project aims to develop the field of Harmonic Analysis, and more precisely to study problems at the interface between Fourier Analysis and PDEs (and also some Geometry). We are interested in two aspects of the Fourier Analysis : (1) The Euclidean Fourier Analysis, where a deep analysis can be performed using specificities as the notion of ``frequencies'' (involving the Fourier transform) or the geometry of the Euclidean balls. By taking advantage of them, this proposal aims to pursue the study and bring novelties in three fashionable topics : the study of bilinear/multilinear Fourier multipliers, the development of the ``space-time resonances'' method in a systematic way and for some specific PDEs, and the study of nonlinear transport equations in BMO-type spaces (as Euler and Navier-Stokes equations). (2) A Functional Fourier Analysis, which can be performed in a more general situation using the notion of ``oscillation'' adapted to a heat semigroup (or semigroup of operators). This second Challenge is (at the same time) independent of the first one and also very close. It is very close, due to the same point of view of Fourier Analysis involving a space decomposition and simultaneously some frequency decomposition. However they are quite independent because the main goal is to extend/develop an analysis in the more general framework given by a semigroup of operators (so without using the previous Euclidean specificities). By this way, we aim to transfer some results known in the Euclidean situation to some Riemannian manifolds, Fractals sets, bounded open set setting, ... Still having in mind some applications to the study of PDEs, such questions make also a connexion with the geometry of the ambient spaces (by its Riesz transform, Poincaré inequality, ...). I propose here to attack different problems as dispersive estimates, ""L^p""-version of De Giorgi inequalities and the study of paraproducts, all of them with a heat semigroup point of view."

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