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Global existence and Computer Assisted Proofs of singularities in incompressible...

Global existence and Computer Assisted Proofs of singularities in incompressible fluids with Applications 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 tra... ver más

30/06/2025

1M€

Presupuesto del proyecto: 1M€

Líder del proyecto

UNIVERSIDAD DE BARCELONA No se ha especificado una descripción o un objeto social para esta compañía.

Total investigadores 327

Ver 2 Participantes

Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2019-12-19

ERC-2019-STG: ERC Starting Grant

I+D

Cerrada hace 6 años

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2 Participantes

1.48M€ | Lider

RELEQUICK

342.36K€ | Participante

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Duración del proyecto: 66 meses Fecha Inicio: 2019-12-19
Fecha Fin: 2025-06-30

Líder del proyecto

UNIVERSIDAD DE BARCELONA No se ha especificado una descripción o un objeto social para esta compañía.

Total investigadores 327

Presupuesto del proyecto 1M€

Descripción del proyecto 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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