Uniform approximation of 2$d$ Navier-Stokes equation by stochastic interacting particle systems
| Autor: | Christian Olivera, Marielle Simon, Franco Flandoli |
|---|---|
| Přispěvatelé: | Dipartimento di Matematica Applicata [Pisa] (DMA), Instituto de Matemática, Estatística e Computação Científica [Brésil] (IMECC), Universidade Estadual de Campinas (UNICAMP), Paradyse, Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), ANR-19-CE40-0012,MICMOV,Microscopic Description of Moving Interfaces, C. O. is partially supported by FAPESP by the grant 2018/15258-7 and by CNPq by the grant 426747/2018-6. This project has received funding from the CNRS-FAPESP cooperation, grant noPRC2726. M.S. also thanks Labex CEMPI (ANR-11-LABX-0007-01), and the ANR grant MICMOV (ANR-19-CE40-0012) of the French National Research Agency (ANR), and finally the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative program (grant agreement no715734)., ANR-19-CE40-0012,MICMOV,Description microscopique des interfaces mobiles(2019), Universidade Estadual de Campinas = University of Campinas (UNICAMP), Systèmes de particules et systèmes dynamiques (Paradyse), Laboratoire Paul Painlevé (LPP), Flandoli, Franco, Olivera, Christian, Simon, Marielle |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Analytic semigroup
2d Navier-Stokes equation 01 natural sciences Moderatly interacting particle system Physics::Fluid Dynamics Stochastic differential equation Mathematics - Analysis of PDEs Vorticity equation FOS: Mathematics 0101 mathematics Empirical process Brownian motion Mathematics Interacting particle system Semigroup Applied Mathematics Probability (math.PR) Mathematical analysis Vorticity Stochastic differ- ential equations Settore MAT/06 - Probabilita' e Statistica Matematica Functional Analysis (math.FA) 010101 applied mathematics Mathematics - Functional Analysis [MATH.MATH-PR]Mathematics [math]/Probability [math.PR] Computational Mathematics Stochastic differential equations Moderately interacting particle system Analysis Mathematics - Probability Analysis of PDEs (math.AP) |
| Zdroj: | SIAM Journal on Mathematical Analysis SIAM Journal on Mathematical Analysis, Society for Industrial and Applied Mathematics, 2020, 52 (6), ⟨10.1137/20M1328993⟩ SIAM Journal on Mathematical Analysis, 2020, 52 (6), ⟨10.1137/20M1328993⟩ |
| ISSN: | 0036-1410 |
| DOI: | 10.1137/20M1328993⟩ |
| Popis: | We consider an interacting particle system modeled as a system of N stochastic differential equations driven by Brownian motions. We prove that the (mollified) empirical process converges, uniformly in time and space variables, to the solution of the two-dimensional Navier-- Stokes equation written in vorticity form. The proofs follow a semigroup approach. We consider an interacting particle system modeled as a system of N stochastic differential equations driven by Brownian motions. We prove that the (mollified) empirical process converges, uniformly in time and space variables, to the solution of the two-dimensional Navier-Stokes equation written in vorticity form. The proofs follow a semigroup approach. |
| Databáze: | OpenAIRE |
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