Non-Newtonian incompressible fluids with nonlinear shear tensor and conditions

Author(s)

Lopez-Lazaro, hereditary Heraclio Ledgar ; Marin-Rubio, Pedro ; Planas, Gabriela

• Document type: Journal article
• Source: COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION; v. 138, p. 20-pg., 2024-07-19.

Abstract

We consider a mathematical model with delay for non-Newtonian incompressible fluids in a bounded domain. Existence of global weak solutions is proved under suitable regularity on the initial data and the forces. Conditions for uniqueness are also given, but in general the results are stated in a multi-valued framework. Suitable multi-valued dynamical systems are well-posed, using basically L-2(Omega)(n) x L-2(-h, 0; L-2(Omega)(n)) or C([-h, 0]; L-2(Omega)(n)) norms. Then the existence of pullback attractors is ensured acting on several universes, some of them of fixed bounded sets and others of tempered type, depending on parameters related to an integrability condition of the force and the delay term. Finally, relationships between these families of attractors are also provided, improving the characterization of attraction with respect to previous results. (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: 19/02512-5 - Systems and partial differential equations
• Grantee: Marcelo da Silva Montenegro
• Support Opportunities: Research Projects - Thematic Grants