Objective
Nonlinear dispersive partial differential equations (PDEs) appear ubiquitously as models describing wave phenomena in various branches of physics and engineering. Over the last few decades, multilinear harmonic analysis has played a crucial role in the development of the theoretical understanding of the subject. Furthermore, in recent years, a non-deterministic point of view has been incorporated into the study of nonlinear dispersive PDEs, enabling us to study typical behaviour of solutions in a probabilistic manner and go beyond the limit of deterministic analysis.
The main objective of this proposal is to develop novel mathematical ideas and techniques, and make significant progress on some of the central problems related to the nonlinear Schrödinger equations (NLS) and the Korteweg-de Vries equation (KdV) from both the deterministic and probabilistic points of view. In particular, we consider the following long term projects:
1. We will study properties of invariant Gibbs measures for nonlinear Hamiltonian PDEs. One project involves establishing a new connection between the limiting behaviour of the Gibbs measures and the concentration phenomena of finite time blowup solutions. The other project aims to understand the space-time covariance of the Gibbs measures in the weakly nonlinear regime.
2. We will first construct the invariant white noise for the cubic NLS on the circle. Then, we will provide a statistical description of the global-in-time dynamics for the stochastic KdV and stochastic cubic NLS on the circle with additive space-time white noise.
3. We will develop novel analytical techniques and construct the local-in-time dynamics for the cubic NLS on the circle in a low regularity.
4. We will advance the understanding of traveling waves and prove scattering for some energy-critical NLS with non-vanishing boundary conditions.
Fields of science (EuroSciVoc)
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
CORDIS classifies projects with EuroSciVoc, a multilingual taxonomy of fields of science, through a semi-automatic process based on NLP techniques. See: The European Science Vocabulary.
- natural sciences mathematics pure mathematics mathematical analysis differential equations partial differential equations
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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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H2020-EU.1.1. - EXCELLENT SCIENCE - 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.
ERC-STG - Starting Grant
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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-2014-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.
EH8 9YL Edinburgh
United Kingdom
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