Existence of weak solutions for a cell-fluid Navier-Stokes model with chemotaxis

• Grant number: 20/14206-3
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: January 01, 2021
• End date: December 31, 2022
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Gabriela Del Valle Planas
• Grantee: Juliana Honda Lopes
• Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil
• Associated research grant: 19/02512-5 - Systems and partial differential equations, AP.TEM

Abstract

The classical Patlak-Keller-Segel system is a typical model that, byreaction-diffusion equations, describes the chemotaxis process. In another hand, the cellscommonly are in an incompressible viscous fluid, then the cells and chemical substrates arealso transported by the fluid. The motion of the fluid is determined by the incompressibleNavier-Stokes equations or Stokes equations, so it is of interest to study a kind of cell-fluidmodel. In the case of Navier-Stokes equations, there are the very well studied Chemotaxis-Navier-Stokes equations. The purpose of this project is to study a general cell-fluid modelintroduced by Qiao and Evje in 2020, which can represent the chemotaxis-Navier-Stokesmodel in a special case. The model involves two mass balance and two momentum balanceequations for the cell and fluid phase, combined with a convection-diffusion-reaction equationfor oxygen.

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)

ZUO, JIABIN; LOPES, JULIANA HONDA. The Kirchhoff-type diffusion problem driven by a magnetic fractional Laplace operator. Journal of Mathematical Physics, v. 63, n. 6, p. 14-pg., 2022-06-01. (20/14206-3)

LOPES, JULIANA HONDA; PLANAS, GABRIELA. EXISTENCE OF SOLUTIONS FOR A NON-ISOTHERMAL NAVIER-STOKES-ALLEN-CAHN SYSTEM WITH THERMO-INDUCED COEFFICIENTS. Electronic Journal of Differential Equations, v. 2022, n. 72, p. 22-pg., 2022-10-25. (20/14206-3, 19/02512-5)

LOPES, JULIANA HONDA; PLANAS, GABRIELA. Existence of weak solutions for a nonhomogeneous incompressible cell-fluid Navier-Stokes model with chemotaxis. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. N/A, p. 21-pg., 2023-04-18. (19/02512-5, 20/14206-3)