Motion of Rigid Bodies of Arbitrary Shape in a Viscous Incompressible Fluid: Wellposedness and Large Time Behaviour

Maity, Debayan; Tucsnak, Marius

doi:10.1007/s00021-023-00814-7

J. Math. Fluid Mech.

2023

DOI: 10.1007/s00021-023-00814-7

|View full text |Cite

Motion of Rigid Bodies of Arbitrary Shape in a Viscous Incompressible Fluid: Wellposedness and Large Time Behaviour

Debayan Maity

Marius Tucsnak

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2024

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Stability of Time-Dependent Motions for Fluid–Rigid Ball Interaction

Hishida

2024

J. Math. Fluid Mech.

View full text Add to dashboard Cite

We aim at the stability of time-dependent motions, such as time-periodic ones, of a rigid body in a viscous fluid filling the exterior to it in 3D. The fluid motion obeys the incompressible Navier–Stokes system, whereas the motion of the body is governed by the balance for linear and angular momentum. Both motions are affected by each other at the boundary. Assuming that the rigid body is a ball, we adopt a monolithic approach to deduce $$L^q$$ L q –$$L^r$$ L r decay estimates of solutions to a non-autonomous linearized system. We then apply those estimates to the full nonlinear initial value problem to find temporal decay properties of the disturbance. Although the shape of the body is not allowed to be arbitrary, the present contribution is the first attempt at analysis of the large time behavior of solutions around nontrivial basic states, that can be time-dependent, for the fluid–structure interaction problem and provides us with a stability theorem which is indeed new even for steady motions under the self-propelling condition or with wake structure.

show abstract

Stability of Time-Dependent Motions for Fluid–Rigid Ball Interaction

Hishida

2024

J. Math. Fluid Mech.

View full text Add to dashboard Cite

show abstract

The vanishing limit of a rigid body in three-dimensional viscous incompressible fluid

He,

2024

Math. Ann.

View full text Add to dashboard Cite

We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space $${{\mathbb {R}}}^3$$ R 3 . When the small rigid body shrinks to a “massless” point in the sense that its density is constant, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier–Stokes equations in the full space. Based on some $$L^p-L^q$$ L p - L q estimates of the fluid–structure semigroup and a fixed point argument, we obtain a uniform estimate of velocity of the rigid body. This allows us to construct admissible test functions which plays a key role in the procedure of passing to the limit.

show abstract

Uniqueness and regularity of weak solutions of a fluid-rigid body interaction system under the Prodi-Serrin condition

Maity,

Takahashi

2024

DCDS

View full text Add to dashboard Cite

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

customersupport@researchsolutions.com

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

This site is protected by reCAPTCHA and the Google Privacy Policy and Terms of Service apply.

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Motion of Rigid Bodies of Arbitrary Shape in a Viscous Incompressible Fluid: Wellposedness and Large Time Behaviour

Cited by 3 publications

References 16 publications

Stability of Time-Dependent Motions for Fluid–Rigid Ball Interaction

Stability of Time-Dependent Motions for Fluid–Rigid Ball Interaction

The vanishing limit of a rigid body in three-dimensional viscous incompressible fluid

Uniqueness and regularity of weak solutions of a fluid-rigid body interaction system under the Prodi-Serrin condition

Contact Info

Product

Resources

About