Discrete and Continuous Dynamical Systems · 2003 · 156 citations · 15 references
Natural SciencesMechanical EngineeringPhysicsComputational Fluid DynamicsFluid DynamicsFluid MechanicsElasticity TheoryFluid-structure InteractionIntegrable SystemsNavier-stokes EquationsPartial Differential EquationsWeak FormulationCoupled Fluid-structure DynamicsCoupled Fluid-structure InteractionEnergy EstimatesFluid - Structure Interaction ModelingFluid-structure Interaction ModelingPressure FieldsStokes Equations
The study examines a time‑dependent Stokes fluid–elastic structure interaction system. The authors introduce a divergence‑free weak formulation that omits the fluid pressure field. They prove existence and uniqueness of a weak solution, establish strong energy estimates under additional data assumptions, and show the pressure field is L²‑integrable after verifying an inf‑sup condition.
A time-dependent system modeling the interaction between a Stokes fluid and an elastic structure is studied. A divergence-free weak formulation is introduced which does not involve the fluid pressure field. The existence and uniqueness of a weak solution is proved. Strong energy estimates are derived under additional assumptions on the data. The existence of an $L^2$ integrable pressure field is established after the verification of an inf-sup condition.
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Acta Applicandae Mathematicae · 1992 · 3.1K citations