Project description
Uncovering the mathematical rules behind turbulence
Understanding how turbulence behaves in fluids is crucial in physics and mathematics, with wide-ranging implications for science and engineering. The ERC-funded MIND project will seek to deepen mathematical understanding of turbulence in incompressible fluids, focusing on two key objectives. First, researchers will investigate linear advection-diffusion equations with singular velocity fields, analysing processes like mixing and energy dissipation that are key to understanding how turbulence forms small-scale structures. Second, the team will delve into nonlinear fluid dynamics, studying equations like Euler and Navier-Stokes, their well-posedness and uniqueness, as well as gradient growth.
Objective
The unifying goal of the MIND project is to enhance the mathematical understanding of turbulence in incompressible fluid mechanics. Turbulence represents one of the most profound unsolved problems in classical physics, giving rise to numerous deep mathematical challenges.
The research is structured around two major interconnected objectives. The first focuses on linear advection-diffusion equations with singular velocity fields, exploring key quantitative aspects such as mixing, enhanced dissipation, and anomalous dissipation. These mechanisms, often easier to isolate and study in linear systems, are crucial for understanding energy transfer and the development of small-scale structures in turbulent fluids.
The second goal addresses nonlinear dynamics in incompressible fluid systems, particularly the Euler, Navier-Stokes equations and the Surface Quasi-Geostrophic (SQG) equation. The main focus will be on the study of weak solutions in relevant function classes and their behavior. We will concentrate on qualitative aspects such as well-posedness and uniqueness, as well as quantitative aspects like gradient growth and anomalous dissipation.
Fields of science (EuroSciVoc)
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Keywords
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Project’s keywords as indicated by the project coordinator. Not to be confused with the EuroSciVoc taxonomy (Fields of science)
Programme(s)
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
Multi-annual funding programmes that define the EU’s priorities for research and innovation.
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HORIZON.1.1 - European Research Council (ERC)
MAIN PROGRAMME
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Topic(s)
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Calls for proposals are divided into topics. A topic defines a specific subject or area for which applicants can submit proposals. The description of a topic comprises its specific scope and the expected impact of the funded project.
Funding Scheme
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
Funding scheme (or “Type of Action”) inside a programme with common features. It specifies: the scope of what is funded; the reimbursement rate; specific evaluation criteria to qualify for funding; and the use of simplified forms of costs like lump sums.
HORIZON-ERC - HORIZON ERC Grants
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Call for proposal
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
Procedure for inviting applicants to submit project proposals, with the aim of receiving EU funding.
(opens in new window) ERC-2025-STG
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Net EU financial contribution. The sum of money that the participant receives, deducted by the EU contribution to its linked third party. It considers the distribution of the EU financial contribution between direct beneficiaries of the project and other types of participants, like third-party participants.
20136 Milano
Italy
The total costs incurred by this organisation to participate in the project, including direct and indirect costs. This amount is a subset of the overall project budget.