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Flows, Waves, and their Asymptotic Stability

Objective

Equations of waves and flows are used extensively in physics and biology, to describe phenomena ranging from the flow past an airfoil, to the collective motion of cells and to the motion of water surface. A major issue is to explain how the propagation through space and the concentration to various scales can emerge from these mathematical models. Fundamental progress have been made since the beginning of the millenium around the role played by specific solutions that either propagate or shrink while keeping the same shape, such as solitary waves for example. These specific solutions are the key to understand the global dynamics. The goal of this project is to push forward the current knowledge on their stability, their emergence over time, and the dynamics they are responsible in several equations. The FloWAS project will study seemingly unrelated models, whose solutions in fact display remarkably close behaviours.

First, we aim at describing how a thin layer of fluid can detach off a boundary and be ejected away in a stream. This is a key phenomenon to understand the drag exerted on moving objects. For this we will study singular solutions of the unsteady Prandtl system of fluid mechanics. Second, we will study concentration phenomena arising in the movement of bacteria. For that we will consider nonlinear structures appearing in the Keller-Segel system: how they can collapse, and how they can interact. Third, we will consider how, from initially disordered wave packets, order appears over time and traveling waves emerge. This study will be made on the critical wave equation. Applications to weak wave turbulence will be pursued. Describing all these phenomena lies at the frontier of current research, and we expect applications to a wide range of models.

Fields of science (EuroSciVoc)

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Keywords

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Programme(s)

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Topic(s)

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Funding Scheme

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HORIZON-ERC - HORIZON ERC Grants

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Call for proposal

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(opens in new window) ERC-2023-STG

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Host institution

CY CERGY PARIS UNIVERSITE
Net EU contribution

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.

€ 1 310 233,00
Address
33 BOULEVARD DU PORT
95011 Cergy-Pontoise
France

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Region
Ile-de-France Ile-de-France Val-d’Oise
Activity type
Higher or Secondary Education Establishments
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Total cost

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.

€ 1 310 233,00

Beneficiaries (1)

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