On the self-similar blowup and existence of determining forms for fractionally dissipative fluids equations

• Grant number: 22/00948-3
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: June 15, 2022
• End date: June 14, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Anne Caroline Bronzi
• Grantee: Ricardo Martins Mendes Guimarães
• Supervisor: Cecilia Freire Mondaini
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Institution abroad: Drexel University, United States
• Associated to the scholarship: 18/22385-5 - On the global well-posedness of hydrodynamic models, BP.DR

Abstract

Our primary goal in this project is the study of locally self-similar solutions for a class of generalized dissipative surface quasi-geostrophic equations where the global well-posedness is still an open problem. We aim to prove an exclusion result of the locally self-similar blowup scenario using similar techniques as we recently developed by Bronzi, Guimarães, Mondaini, for a special case of these equations. As a secondary goal, we plan to investigate the existence of the notion of determining forms for the strongly damped Euler equations, particularly inspired by the approach developed by Biswas, Foias, Mondaini and Titi. (AU)