National research project founded by the UEFISCDI (Ministerul Cercetarii si Inovarii,
Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii)
PN-IV-P2-2.1-T-TE-2023-1704
Project leader: Oana-Valeria STAMATE (LUPASCU)
Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics
of the Romanian Academy
Period : August 2025 - July 2027
The project will develop stochastic and numerical methods for the study of boundary effects in nonlinear partial differential equations with physical relevance. We will use infinite dimensional stochastic analysis tools, in particular, measure-valued branching Markov processes.
We will provide probabilistic representations for solutions of Navier-Stokes equations in bounded planar domains through an appropriate nonlocal branching process and prove the convergence of the corresponding numerical algorithm. In the case of less regular domains, such as Lipschitz or polygonal domains we will provide an intuitive understanding of how the loss of regularity is related to the geometry of the domain through the branching process.
Moreover, we will provide a probabilistic representation for the solutions of nonlinear Neumann boundary problems and corresponding numerical algorithms. Using stochastic differential equations we will derive probabilistic interpretations fragmentation and coagulation processes in duality. These will be applied to the study of avalanche models.
Project Leader:
Dr. Oana-Valeria STAMATE (LUPASCU)
Researcher Members:
Drd. Ana-Maria Boengiu
Dr. Iulian Cimpean
Dr. Catalin Vrabie
Dr. Arghir Dani Zarnescu
Papers:
Xingyu Li and Arghir Zarnescu, ``Patterns in a Smoluchowski Equation", acceptat la Communications in Contemporary Mathematics
M. Deaconu, O. Lupascu-Stamate, Asymptotic behavior of a one-dimensional avalanche model through a particular stochastic process, REVUE ROUMAINE DE MATHÉMATIQUES PURES ET APPLIQUÉES , 2025.
Preprints:
Iulian Cimpean, Ionut Popescu, Arghir Zarnescu, "Quantitative boundary Holder estimates for the inhomogeneous, Poisson problem through a probabilistic approach", arXiv:2510.06906
Simone Rusconi, Christina Schenkb, Razvan Ceuca, Arghir Zarnescu, Elena Akhmatskaya, ``Complexity reduction of physical models: an equation-free approach by means of scaling", arXiv:2506.05029
D. Coculescu, O. Lupascu-Stamate, G. Visentin, On the fragility of mutual insurance arrangements, 2025
Talks in international conferences:
Arghir Zarnescu, Electric field effects in nematic liquid crystals, COMPLAS 2025 Conference, Barcelona, Spania, Septembrie 2025
Arghir Zarnescu, A Variational Approach to Fluids, WADE25 Conference, Varsovia, Polonia, Septembrie 2025
Oana Lupascu-Stamate, Mathematical modeling of the dense avalanche onset , The 32st Conference on Applied and Industrial Mathematics, 18-21 septembrie 2025, Bucuresti
Oana Lupascu-Stamate, Mathematical modeling of the dense avalanche onset ,The 41st “Caius IACOB” Conference on Fluid Mechanics and its Technical Applications, 30 - 31 Octombrie, 2025, Bucuresti
Oana Lupascu-Stamate, Curgerea unei avalanse de zapada ,Matematica si Scoala, III, Scoala Gimnaziala Mihai Eminescu, 20 noiembrie 2025, Pitesti (outreach conference)
Oana Lupascu-Stamate, Mathematical modeling of the dense avalanche onset on a surface with topography, Seminar ISMMA, 14 October, 2025