Global Low-Energy Weak Solutions of a Fluid–Particle Interaction Model with Vacuum in R3

Key Points

• The aim is to establish the existence of global-in-time weak solutions for fluid-particle interaction systems in the presence of vacuum.
• Analyzed initial data characterized by small energy around a steady state.
• Utilized mathematical techniques to handle fluid-particle interactions under certain conditions.
• Considered systems where vacuum is present to assess solution behavior.
• Established conditions under which global weak solutions exist.
• Proved that solutions can persist over time despite the presence of vacuum.
• Showed that weak solutions maintain consistency with initial conditions.