The Existence of the Global Generalized Solution of the System of Equations Describing Suspension Motion, Mathematical Methods in the Applied Sciences, vol.6, issue.6, pp.495-519, 1997. ,
DOI : 10.1002/(SICI)1099-1476(199704)20:6<495::AID-MMA858>3.0.CO;2-O
A Modeling of Biospray for the Upper Airways, CEMRACS 2004 ? Mathematics and applications to biology and medicine, pp.41-47, 2005. ,
DOI : 10.1051/proc:2005004
COUPLING EULER AND VLASOV EQUATIONS IN THE CONTEXT OF SPRAYS: THE LOCAL-IN-TIME, CLASSICAL SOLUTIONS, Journal of Hyperbolic Differential Equations, vol.03, issue.01, pp.1-26, 2006. ,
DOI : 10.1142/S0219891606000707
Probl??mes aux limites pour les ??quations aux d??riv??es partielles du premier ordre ?? coefficients r??els; th??or??mes d'approximation; application ?? l'??quation de transport, Annales scientifiques de l'??cole normale sup??rieure, vol.3, issue.2, pp.185-233, 1970. ,
DOI : 10.24033/asens.1190
EXISTENCE THEORY FOR THE KINETIC-FLUID COUPLING WHEN SMALL DROPLETS ARE TREATED AS PART OF THE FLUID, Journal of Hyperbolic Differential Equations, vol.11, issue.01, pp.109-133, 2014. ,
DOI : 10.1142/S0219891614500027
URL : https://hal.archives-ouvertes.fr/hal-00805104
Fluid-Particles Flows: A Thin Spray Model with Energy
Exchanges, CEMRACS 2008?Modelling and numerical simulation of complex fluids, pp.195-210, 2009. ,
DOI : 10.1051/proc/2009047
URL : https://hal.archives-ouvertes.fr/inria-00543156
Global existence of solutions for the coupled Vlasov and Navier-Stokes equations, Differential Integral Equations, vol.22, pp.11-121247, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-00331895
A Modeling of Compressible Droplets in a Fluid, Communications in Mathematical Sciences, vol.1, issue.4, pp.657-669, 2003. ,
DOI : 10.4310/CMS.2003.v1.n4.a2
Abstract, Communications in Computational Physics, vol.42, issue.03, pp.723-756, 2015. ,
DOI : 10.1080/02786820119122
Trace theorems and spatial continuity properties for the solutions of the transport equation, Differential Integral Equations, vol.18, issue.8, pp.891-934, 2005. ,
URL : https://hal.archives-ouvertes.fr/hal-00004420
Mathematical tools for the study of the incompressible Navier-Stokes equations and related models, Applied Mathematical Sciences, vol.183, 2013. ,
DOI : 10.1007/978-1-4614-5975-0
URL : https://hal.archives-ouvertes.fr/hal-00777731
Global classical solutions close to equilibrium to the Vlasov-Fokker-Planck-Euler system, Kinetic and Related Models, vol.4, issue.1, pp.227-258, 2011. ,
DOI : 10.3934/krm.2011.4.227
URL : https://hal.archives-ouvertes.fr/hal-00652339
Global existence of weak and classical solutions for the Navier???Stokes???Vlasov???Fokker???Planck equations, Journal of Differential Equations, vol.251, issue.9, pp.2431-2465, 2011. ,
DOI : 10.1016/j.jde.2011.07.016
GLOBAL CLASSICAL SOLUTIONS FOR A COMPRESSIBLE FLUID-PARTICLE INTERACTION MODEL, Journal of Hyperbolic Differential Equations, vol.10, issue.03, pp.537-562, 2013. ,
DOI : 10.1142/S0219891613500197
Some aspects of the modeling at different scales of multiphase flows, Computer Methods in Applied Mechanics and Engineering, vol.199, issue.21-22, pp.21-221265, 2010. ,
DOI : 10.1016/j.cma.2009.08.008
Ordinary differential equations, transport theory and Sobolev spaces, Inventiones Mathematicae, vol.307, issue.3, pp.511-547, 1989. ,
DOI : 10.1007/BF01393835
Modélisation multi-fluide eulérienne pour les écoulements diphasiques à inclusions dispersées, 2005. ,
On existence of weak solutions of the Navier-Stokes equations in regions with moving boundaries, J. Fac. Sci. Univ. Tokyo Sect. I, vol.17, pp.403-420, 1970. ,
A Numerical and Experimental Study of Spray Dynamics in a Simple Throat Model, Aerosol Science and Technology, vol.9, issue.1, pp.18-38, 2002. ,
DOI : 10.1080/02786829708965417
Elliptic partial differential equations of second order, of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences, 1983. ,
The Navier???Stokes???Vlasov???Fokker???Planck System near Equilibrium, SIAM Journal on Mathematical Analysis, vol.42, issue.5, pp.2177-2202, 2010. ,
DOI : 10.1137/090776755
URL : https://hal.archives-ouvertes.fr/inria-00384364
Hydrodynamic limit for the Vlasov-Navier-Stokes equations. Part I: Light particles regime., Indiana University Mathematics Journal, vol.53, issue.6, pp.1495-1515, 2004. ,
DOI : 10.1512/iumj.2004.53.2508
URL : https://hal.archives-ouvertes.fr/hal-00018815
Hydrodynamic limit for the Vlasov-Navier-Stokes equations. Part II: Fine particles regime., Indiana University Mathematics Journal, vol.53, issue.6, pp.1517-1536, 2004. ,
DOI : 10.1512/iumj.2004.53.2509
URL : https://hal.archives-ouvertes.fr/hal-00018815
Global existence and large time behaviour of solutions for the Vlasov-Stokes equations, Japan Journal of Industrial and Applied Mathematics, vol.17, issue.1, pp.51-74, 1998. ,
DOI : 10.1007/BF03167396
Global well-posedness and large time behavior of strong solution to a kinetic-fluid model. ArXiv e-prints, 2015. ,
Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, 1969. ,
LOCAL SMOOTH SOLUTIONS OF A THIN SPRAY MODEL WITH COLLISIONS, Mathematical Models and Methods in Applied Sciences, vol.20, issue.02, pp.191-221, 2010. ,
DOI : 10.1142/S0218202510004192
GLOBAL WEAK SOLUTIONS FOR A VLASOV???FOKKER???PLANCK/NAVIER???STOKES SYSTEM OF EQUATIONS, Mathematical Models and Methods in Applied Sciences, vol.17, issue.07, pp.1039-1063, 2007. ,
DOI : 10.1142/S0218202507002194
Asymptotic Analysis for a Vlasov-Fokker-Planck/ Compressible Navier-Stokes System of Equations, Communications in Mathematical Physics, vol.22, issue.1, pp.573-596, 2008. ,
DOI : 10.1007/s00220-008-0523-4
On The Trace Problem For Solutions Of The Vlasov Equation, Communications in Partial Differential Equations, vol.314, issue.7-8, pp.1415-1443, 2000. ,
DOI : 10.1007/BF01837113
Some variants of the classical Aubin???Lions Lemma, Journal of Evolution Equations, vol.146, issue.4, pp.65-93, 2016. ,
DOI : 10.1007/s00028-015-0293-3
URL : https://hal.archives-ouvertes.fr/hal-01300507
On a Vlasov-Euler system for 2D sprays with gyroscopic effects, Asymptot. Anal, vol.81, issue.1, pp.53-91, 2013. ,
Collective drop effects on vaporizing liquid sprays, 1981. ,
On the existence of weak solutions of a nonlinear mixed problem for the Navier-Stokes equations in a time dependent domain, J. Fac. Sci. Univ. Tokyo Sect. IA Math, vol.32, issue.2, pp.213-221, 1985. ,
Navier Stokes Equations: Theory and Numerical Analysis, Journal of Applied Mechanics, vol.45, issue.2, 2001. ,
DOI : 10.1115/1.3424338
Global weak solution to the inhomogeneous Navier???Stokes???Vlasov equations, Journal of Differential Equations, vol.259, issue.8, pp.3976-4008, 2015. ,
DOI : 10.1016/j.jde.2015.05.016
Combustion theory, Benjamin Cummings, 1985. ,
URL : https://hal.archives-ouvertes.fr/hal-00014918
Global weak solutions to the incompressible Navier???Stokes???Vlasov equations, Journal de Math??matiques Pures et Appliqu??es, vol.100, issue.2, pp.275-293, 2013. ,
DOI : 10.1016/j.matpur.2013.01.001
F-78153 Le Chesnay Cedex, France E-mail address: laurent.boudin@upmc.fr C.G.: Inria, EPC Reo, F-78153 Le Chesnay Cedex E-mail address: celine.grandmont@inria, p.75005 ,