PDEs and time-dependent gradient flows in rough spaces

• Grant number: 16/16104-8
• Support Opportunities: Regular Research Grants
• Start date: November 01, 2016
• End date: January 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Lucas Catão de Freitas Ferreira
• Grantee: Lucas Catão de Freitas Ferreira
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This project has basically two parts. In the first, we approach partial differential equations (PDEs) in rough spaces, such as weighted-Lp spaces (and sum of them), Morrey spaces, pseudomeasure spaces, Besov spaces, Fourier-Besov spaces, Fourier-Besov-Morrey spaces, Herz type spaces, Besov-Morrey spaces, and investigate the issues of existence, uniqueness, symmetries, renormalization, stability and asymptotic behavior of solutions. The second part consists in studying time-dependent gradient flows in metric spaces and looking for a general theory that can be applied to a number of PDEs and connected with the optimal mass transport theory and Wasserstein space. (AU)

Scientific publications

(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)

BENVENUTTI, MAICON J.; FERREIRA, LUCAS C. F.. Global stability of large solutions for the Navier-Stokes equations with Navier boundary conditions. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, v. 43, p. 308-322, OCT 2018. (16/16104-8, 13/21819-8)

FERREIRA, LUCAS C. F.; FERREIRA, JR., VANDERLEY A.. ON THE EVENTUAL LOCAL POSITIVITY FOR POLYHARMONIC HEAT EQUATIONS. Proceedings of the American Mathematical Society, v. 147, n. 10, p. 4329-4341, OCT 2019. (16/16104-8, 16/06209-7)

FERREIRA, L. C. F.; SANTOS, M. C.; VALENCIA-GUEVARA, J. C.. Minimizing movement for a fractional porous medium equation in a periodic setting. BULLETIN DES SCIENCES MATHEMATIQUES, v. 153, p. 86-117, JUL 2019. (16/16104-8, 14/23326-1)