Nonlinear dynamical analysis for globally modified incompressible non-Newtonian fluids

Author(s)

Caraballo, Tomas ; Carvalho, Alexandre N. ; Lopez-Lazaro, Heraclio

• Document type: Journal article
• Source: Journal of Mathematical Physics; v. 64, n. 11, p. 29-pg., 2023-11-01.

Abstract

We present the global modification of the Ladyzhenskaya equations, for incompressible non-Newtonian fluids. This modification is through a cut-off function that multiplies the convective term of the equation and an additional artificial smoothing dissipation term as part of the viscous term of the equation. The goal of this work is the comparative analysis between the modified system and the non-modified system. Therefore, we show the existence and regularity of weak solutions, the existence of global attractors, the estimation of the fractal dimension of the global attractors, and finally, the relationship of the autonomous dynamics between the modified system and the non-modified system. (AU)

• FAPESP's process: 21/01931-4 - Pullback attractor for non-linear parabolic equations with subdifferential principal part
• Grantee: Heraclio Ledgar López Lázaro
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• FAPESP's process: 22/13001-4 - Finite fractal dimension for non-linear parabolic equations with subdifferential principal part
• Grantee: Heraclio Ledgar López Lázaro
• Support Opportunities: Scholarships abroad - Research Internship - Post-doctor
• FAPESP's process: 20/14075-6 - Dynamical systems and their attractors under perturbations
• Grantee: Alexandre Nolasco de Carvalho
• Support Opportunities: Research Projects - Thematic Grants