EXISTENCE THEORY FOR THE KINETIC-FLUID COUPLING WHEN SMALL DROPLETS ARE TREATED AS PART OF THE FLUID

DOI10.1142/S0219891614500027zbMath1293.35020arXiv1303.6527OpenAlexW4302567041MaRDI QIDQ5415588

Ayman Moussa, Saad Benjelloun, Laurent Desvillettes

Publication date: 13 May 2014

Published in: Journal of Hyperbolic Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.6527

zbMATH Keywords

Vlasov-Boltzmann equationDiPerna-Lions theory

Mathematics Subject Classification ID

Singular perturbations in context of PDEs (35B25) Navier-Stokes equations (35Q30) Liquid-gas two-phase flows, bubbly flows (76T10)

Related Items (14)

Global solutions and exponential time decay rates to the Navier–Stokes–Vlasov–Fokker–Planck system in low regularity space ⋮ Uniqueness of the solution to the 2D Vlasov-Navier-Stokes system ⋮ Strong solutions to the inhomogeneous Navier-Stokes-BGK system ⋮ Global weak solutions to the inhomogeneous incompressible Navier-Stokes-Vlasov-Boltzmann equations ⋮ Strong Solutions to the Compressible Navier--Stokes--Vlasov--Fokker--Planck Equations: Global Existence Near the Equilibrium and Large Time Behavior ⋮ Global weak solutions for a Vlasov-Fokker-Planck/Navier-Stokes system with nonhomogeneous boundary data ⋮ The Vlasov-Navier-Stokes system in a 2D pipe: existence and stability of regular equilibria ⋮ Existence of global weak solutions for the Navier-Stokes-Vlasov-Boltzmann equations ⋮ Global existence of solutions to the incompressible Navier-Stokes-Vlasov equations in a time-dependent domain ⋮ Global well-posedness and large time behavior of classical solutions to the Vlasov-Fokker-Planck and magnetohydrodynamics equations ⋮ Asymptotic analysis for 1D compressible Navier-Stokes-Vlasov equations ⋮ Global well-posedness and optimal large-time behavior of strong solutions to the non-isentropic particle-fluid flows ⋮ Global weak solution to the inhomogeneous Navier-Stokes-Vlasov equations ⋮ Some variants of the classical Aubin-Lions lemma

Cites Work

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• Elliptic partial differential equations of second order
• Global existence and large time behaviour of solutions for the Vlasov-Stokes equations
• Asymptotic analysis for a Vlasov-Fokker-Planck compressible Navier-Stokes system of equations
• COUPLING EULER AND VLASOV EQUATIONS IN THE CONTEXT OF SPRAYS: THE LOCAL-IN-TIME, CLASSICAL SOLUTIONS
• LOCAL SMOOTH SOLUTIONS OF A THIN SPRAY MODEL WITH COLLISIONS
• GLOBAL WEAK SOLUTIONS FOR A VLASOV–FOKKER–PLANCK/NAVIER–STOKES SYSTEM OF EQUATIONS

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