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CAPA SIGNED

Global existence and Computer-Assisted Proofs of singularities in incompressible fluids, with Applications

Total Cost €

0

EC-Contrib. €

0

Partnership

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Project "CAPA" data sheet

The following table provides information about the project.

Coordinator
UNIVERSITAT DE BARCELONA 

Organization address
address: GRAN VIA DE LES CORTS CATALANES 585
city: BARCELONA
postcode: 8007
website: http://www.ub.es

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Spain [ES]
 Total cost 1˙483˙073 €
 EC max contribution 1˙483˙073 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2019-STG
 Funding Scheme ERC-STG
 Starting year 2020
 Duration (year-month-day) from 2020-07-01   to  2025-06-30

 Partnership

Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 
1    UNIVERSITAT DE BARCELONA ES (BARCELONA) coordinator 1˙483˙073.00

Map

 Project objective

The goal of this proposal is twofold: on the one hand to pursue methods and ideas developed in recent work in the search for either singularities or global existence in incompressible fluids with finite energy and on the other transfer the techniques to solve long-standing open problems in spectral geometry. A key ingredient in its success is to have accurate numerics together with a deep understanding of the regularity theory. Therefore, the interdisciplinary nature of this project, which involves numerical computations, computer-assisted proofs, modern PDE methods and harmonic analysis, is an essential ingredient for the successful outcome. This proposal is divided in three blocks, the first two involving global existence and/or singularities for: the incompressible Euler and Navier-Stokes equations; the surface quasi-geostrophic (SQG), the generalized-SQG equations and related models; and a third one on applications to spectral geometry. There is a strong analogy between the SQG and the 3D Euler equations, and many results that hold for the former also hold for the latter. A major theme is the interplay between rigorous computer calculations and traditional mathematics. Interval arithmetics are used as part of a proof whenever they are needed. As an evidence of its capabilities, I have pioneered techniques to show singularities in PDE related to fluid mechanics – even in low regularity settings –, developed a way to treat singular integrals, and solved eigenvalue problems using computer-assisted proofs. This is a completely novel approach that can be blended with more classical ones, resulting in very powerful theorems solving problems that can not be treated currently with pen and paper methods.

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The information about "CAPA" are provided by the European Opendata Portal: CORDIS opendata.

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