Existence and properties of solutions for chemotaxis fluid models

• Grant number: 19/02733-1
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: May 01, 2019
• End date: April 30, 2023
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Lucas Catão de Freitas Ferreira
• Grantee: Daniel Pires Araujo Lima
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

In this project we consider fluid models with biological interactions of chemotaxis type. We analyse issues such as existence, uniqueness, formation of singularities, solutions without regularity of Sobolev type, self-similarity, stability and asymptotic behavior. The basic strategy is to study the models in different functional spaces with low regularity that allow solutions with the desired properties. (AU)