Stochastic Partial Differential Equations and Particle Systems

• Grant number: 17/17670-0
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2017
• End date: October 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Christian Horacio Olivera
• Grantee: Christian Horacio Olivera
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated researchers: Ciprian Tudor ; David Alexander Chipana Mollinedo ; Jean-François Claude Colombeau ; Jorge Clarke ; Marielle Simon ; Pedro Jose Catuogno
• Associated research grant(s): 18/15258-7 - Approximation of partial differential equations by stochastic particle systems with weak and moderate interaction, AP.R SPRINT

Abstract

This research project presents in a global way the research interests of the proponent team. In fact, we are interested in studying existence, uniqueness and regularity in the law of stochastic partial differential equations.Another important part of the project is to study the propagation of chaos of particle systems with moderate interaction. (AU)

Scientific publications

(14)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

OLIVERA, CHRISTIAN. Regularization by Noise in One-Dimensional Continuity Equation. POTENTIAL ANALYSIS, v. 51, n. 1, p. 23-35, JUL 2019. (17/17670-0)

MOLLINEDO, DAVID A. C.; OLIVERA, CHRISTIAN; TUDOR, CIPRIAN A.. Existence and Smoothness of the Density for the Stochastic Continuity Equation. Results in Mathematics, v. 74, n. 1, MAR 2019. (15/07278-0, 17/17670-0)

OLIVERA, CHRISTIAN. Well-posedness of the non-local conservation law by stochastic perturbation. MANUSCRIPTA MATHEMATICA, v. 162, n. 3-4, p. 367-387, JUL 2020. (15/07278-0, 17/17670-0)

NEVES, WLADIMIR; OLIVERA, CHRISTIAN. Initial-boundary value problem for stochastic transport equations. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, v. 9, n. 3, p. 674-701, SEP 2021. (15/07278-0, 17/17670-0, 13/15795-9)

OLIVERA, CHRISTIAN; SHAMAROVA, EVELINA. Gaussian density estimates for solutions of fully coupled forward-backward SDEs. Mathematische Nachrichten, v. 293, n. 8, p. 11-pg., 2020-05-25. (17/17670-0, 15/07278-0)

NEVES, WLADIMIR; OLIVERA, CHRISTIAN. Initial-boundary value problem for stochastic transport equations. STOCHASTICS AND PARTIAL DIFFERENTIAL EQUATIONS-ANALYSIS AND COMPUTATIONS, SEP 2020. (13/15795-9, 15/07278-0, 17/17670-0)

OLIVERA, CHRISTIAN; TUDOR, CIPRIAN A.. Existence and Besov regularity of the density for a class of SDEs with Volterra noise. COMPTES RENDUS MATHEMATIQUE, v. 357, n. 7, p. 636-645, JUL 2019. (15/07278-0, 17/17670-0)

FERRARIO, BENEDETTA; OLIVERA, CHRISTIAN. 2D Navier-Stokes equation with cylindrical fractional Brownian noise. Annali di Matematica Pura ed Applicata, v. 198, n. 3, p. 1041-1067, JUN 2019. (15/07278-0, 17/17670-0)

CLARKE, JORGE; OLIVERA, CHRISTIAN. LOCAL L-p-SOLUTION FOR SEMILINEAR HEAT EQUATION WITH FRACTIONAL NOISE. ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, v. 45, p. 305-312, 2020. (15/07278-0, 17/17670-0)

OLIVERA, CHRISTIAN; TUDOR, CIPRIAN. Density for solutions to stochastic differential equations with unbounded drift. BRAZILIAN JOURNAL OF PROBABILITY AND STATISTICS, v. 33, n. 3, p. 520-531, AUG 2019. (15/07278-0, 17/17670-0)

OLIVERA, CHRISTIAN; SHAMAROVA, EVELINA. Gaussian density estimates for solutions of fully coupled forward-backward SDEs. Mathematische Nachrichten, v. 293, n. 8, p. 1554-1564, AUG 2020. (17/17670-0, 15/07278-0)

FERRARIO, BENEDETTA; OLIVERA, CHRISTIAN. L-p-solutions of the Navier-Stokes equation with fractional Brownian noise. AIMS MATHEMATICS, v. 3, n. 4, p. 539-553, 2018. (15/07278-0, 17/17670-0)

OLIVERA, CHRISTIAN. Probabilistic representation for mild solution of the Navier-Stokes equations. MATHEMATICAL RESEARCH LETTERS, v. 28, n. 2, p. 563-573, 2021. (15/07278-0, 17/17670-0)

DE LA CRUZ, H.; OLIVERA, C.. An explicit numerical scheme for the computer simulation of the stochastic transport equation. COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, v. 110, p. 14-pg., 2022-07-01. (17/17670-0, 15/07278-0)