A no-contact result for a plate-fluid interaction system in dimension three

2025/10/11 by Bukal, Mario, Kukavica, Igor, Li, Linfeng +1 · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2510.09992

Abstract

We address the fluid-structure interaction between a viscous incompressible fluid and an elastic plate forming its moving upper boundary in three dimensions. The fluid is described by the incompressible Navier-Stokes equations with a free upper boundary that evolves according to the motion of the structure, coupled via the velocity- and stress-matching conditions. Under the natural energy bounds and additional regularity assumptions on the weak solutions, we prove a non-contact property with a uniform separation of the plate from the rigid boundary. The result does not require damping in the plate equation.

Citations

• A global existence result on weak solutions for the 3D Navier-Stokes-plate system with no contact
• Compressible fluids and elastic plates in 2D: A conditional no-contact theorem
• Inviscid fluid interacting with a nonlinear two-dimensional plate
• Global weak solutions to a 3D/3D fluid-structure interaction problem including possible contacts
• On an existence theory for a fluid-beam problem encompassing possible\n contacts
• Existence of a weak solution to the fluid-structure interaction problem in 3D

Cited by

• Exponential Decay of Solutions to a Fluid-Plate Model with Small Initial Data
• A global existence result on weak solutions for the 3D Navier-Stokes-plate system with no contact

Related

• A global existence result on weak solutions for the 3D Navier-Stokes-plate system with no contact
• Compressible fluids and elastic plates in 2D: A conditional no-contact theorem
• Existence of a weak solution to the fluid-structure interaction problem in 3D
• A free boundary inviscid model of flow-structure interaction
• A uniqueness result for 3D incompressible fluid-rigid body interaction problem