Global existence of strong solutions to the Cucker-Smale-Stokes system

DOI10.1007/s00021-015-0237-2zbMath1383.35152OpenAlexW2239031394MaRDI QIDQ2629307

Young-Pil Choi, Moon-Jin Kang, Hyeong-Ohk Bae, Seung-Yeal Ha

Publication date: 6 July 2016

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00021-015-0237-2

zbMATH Keywords

Stokes equationsCucker-Smale modelVlasov equationskinetic-fluid equations

Mathematics Subject Classification ID

Interacting particle systems in time-dependent statistical mechanics (82C22) PDEs in connection with fluid mechanics (35Q35) Stokes and related (Oseen, etc.) flows (76D07) Vlasov equations (35Q83) Strong solutions to PDEs (35D35) PDEs in connection with statistical mechanics (35Q82)

Related Items

On the global existence of weak solutions for the Cucker-Smale-Navier-Stokes system with shear thickening ⋮ Optimal energy decay rate for a kinetic equation coupled with the Stokes equations ⋮ Global existence of strong solutions to the kinetic Cucker-Smale model coupled with the two dimensional incompressible Navier-Stokes equations ⋮ The global existence of strong solutions to thermomechanical Cucker-Smale-Stokes equations in the whole domain ⋮ Solvability and blow-up criterion of the thermomechanical Cucker-Smale-Navier-Stokes equations in the whole domain ⋮ Global dynamics of the thermomechanical Cucker–Smale ensemble immersed in incompressible viscous fluids ⋮ On the coupling of kinetic thermomechanical Cucker-Smale equation and compressible viscous fluid system ⋮ Temporal decays and asymptotic behaviors for a Vlasov equation with a flocking term coupled to incompressible fluid flow ⋮ Global existence of strong solutions to the kinetic Cucker–Smale model coupled with the Stokes equations

Cites Work

• Asymptotic flocking dynamics of Cucker-Smale particles immersed in compressible fluids
• Global existence of solutions for the coupled Vlasov and Navier-Stokes equations.
• Global existence of weak and classical solutions for the Navier-Stokes-Vlasov-Fokker-Planck equations
• Regularity of coupled two-dimensional nonlinear Fokker-Planck and Navier-Stokes systems
• Global existence of weak and strong solutions to Cucker-Smale-Navier-Stokes equations in \(\mathbb{R}^2\)
• From particle to kinetic and hydrodynamic descriptions of flocking
• Continuity of velocity gradients in suspensions of rod-like molecules
• Abstract \(L^ p\) estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains
• Global existence of strong solution for the Cucker-Smale-Navier-Stokes system
• Two-species flocking particles immersed in a fluid
• Global existence and large time behaviour of solutions for the Vlasov-Stokes equations
• Global regularity of solutions of coupled Navier-Stokes equations and nonlinear Fokker Planck equations
• Time-asymptotic interaction of flocking particles and an incompressible viscous fluid
• A hydrodynamic model for the interaction of Cucker–Smale particles and incompressible fluid
• Global well-posedness and large-time behavior for the inhomogeneous Vlasov–Navier–Stokes equations
• On the analysis of a coupled kinetic-fluid model with local alignment forces