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Global existence of weak solutions to the incompressible Vlasov-Navier-Stokes system coupled to convection-diffusion equations. (English) Zbl 1450.35211
MSC:
35Q35 PDEs in connection with fluid mechanics
35Q83 Vlasov equations
35D30 Weak solutions to PDEs
76D05 Navier-Stokes equations for incompressible viscous fluids
76R50 Diffusion
76T10 Liquid-gas two-phase flows, bubbly flows
76T30 Three or more component flows
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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[1] Anoshchenko, O. and de Monvel-Berthier, A. Boutet, The existence of the global generalized solution of the system of equations describing suspension motion, Math. Methods Appl. Sci.20 (1997) 495-519. · Zbl 0871.35075
[2] Baranger, C., Boudin, L., Jabin, P.-E. and Mancini, S., A modeling of biospray for the upper airways, in CEMRACS 2004 — Mathematics and Applications to Biology and Medicine, , Vol. 14 (EDP Sciences, 2005), pp. 41-47. · Zbl 1075.92031
[3] Baranger, C. and Desvillettes, L., Coupling Euler and Vlasov equations in the context of sprays: The local-in-time, classical solutions, J. Hyperbolic Differ. Equ.3 (2006) 1-26. · Zbl 1093.35046
[4] F. F. Bonsall, Lectures on Some Fixed Point Theorems of Functional Analysis, Notes by K. B. Vedak (Tata Institute of Fundamental Research, 1962).
[5] Boudin, L., Desvillettes, L., Grandmont, C. and Moussa, A., Global existence of solutions for the coupled Vlasov and Navier-Stokes equations, Differential Integral Equ.22 (2009) 1247-1271. · Zbl 1240.35403
[6] Boudin, L., Grandmont, C., Grec, B., Martin, S., Mecherbet, A. and Noël, F., Fluid-kinetic modelling for respiratory aerosols with variable size and temperature, ESAIM Proc. Surveys67 (2020) 100-119. · Zbl 1446.76168
[7] Boudin, L., Grandmont, C., Lorz, A. and Moussa, A., Modelling and numerics for respiratory aerosols, Commun. Comput. Phys.18 (2015) 723-756. · Zbl 1373.76078
[8] Boudin, L., Grandmont, C. and Moussa, A., Global existence of solutions to the incompressible Navier-Stokes-Vlasov equations in a time-dependent domain, J. Differential Equations262 (2017) 1317-1340. · Zbl 1371.35214
[9] Chae, M., Kang, K. and Lee, J., Global classical solutions for a compressible fluid-particle interaction model, J. Hyperbolic Differ. Equ.10 (2013) 537-562. · Zbl 1284.35305
[10] Y.-P. Choi and J. Jung, Asymptotic analysis for Vlasov-Fokker-Planck/compressible Navier-Stokes equations with a density-dependent viscosity, preprints (2019), arXiv:1901.01221.
[11] Desvillettes, L., Some aspects of the modeling at different scales of multiphase flows, Comput. Methods Appl. Mech. Engrg.199 (2010) 1265-1267. · Zbl 1227.76067
[12] DiPerna, R. J. and Lions, P.-L., Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math.98 (1989) 511-547. · Zbl 0696.34049
[13] Dufour, G. and Villedieu, P., A second-order multi-fluid model for evaporating sprays, M2AN Math. Model. Numer. Anal.39 (2005) 931-963. · Zbl 1075.35048
[14] Evans, L. C., Partial Differential Equations, , 2nd edn. Vol. 19 (Amer. Math. Soc., 2010). · Zbl 1194.35001
[15] Gemci, T., Corcoran, T. and Chigier, N., A numerical and experimental study of spray dynamics in a simple throat model, Aerosol Sci. Technol.36 (2002) 18-38.
[16] Glass, O., Han-Kwan, D. and Moussa, A., The Vlasov-Navier-Stokes system in a 2D pipe: Existence and stability of regular equilibria, Arch. Ration. Mech. Anal.230 (2018) 593-639. · Zbl 1398.35242
[17] Hamdache, K., Global existence and large time behavior of solutions for the Vlasov-Stokes equations, Japan J. Indust. Appl. Math.15 (1998) 51-74. · Zbl 1306.76052
[18] Han-Kwan, D., Miot, É., Moussa, A. and Moyano, I., Uniqueness of the solution to the 2D Vlasov-Navier-Stokes system, Rev. Mat. Iberoam.36 (2020) 37-60. · Zbl 1437.35536
[19] D. Han-Kwan, A. Moussa and I. Moyano, Large time behavior of the Vlasov-Navier-Stokes system on the torus, To appear in Arch. Ration. Mech. Anal. · Zbl 1436.35043
[20] Li, F., Mu, Y. and Wang, D., Strong solutions to the compressible Navier-Stokes-Vlasov-Fokker-Planck equations: Global existence near the equilibrium and large time behavior, SIAM J. Math. Anal.49(2) (2017) 984-1026. · Zbl 1367.35110
[21] Longest, P. W. and Hindle, M., Numerical model to characterize the size increase of combination drug and hygroscopic excipient nanoparticle aerosols, Aerosol Sci. Tech.45 (2011) 884-899.
[22] Mathiaud, J., Local smooth solutions of a thin spray model with collisions, Math. Models Methods Appl. Sci.20 (2010) 191-221. · Zbl 1225.35175
[23] Mellet, A. and Vasseur, A., Global weak solutions for a Vlasov-Fokker-Planck/ Navier-Stokes system of equations, Math. Models Methods Appl. Sci.17 (2007) 1039-1063. · Zbl 1136.76042
[24] Mellet, A. and Vasseur, A., Asymptotic analysis for a Vlasov-Fokker-Planck/compressible Navier-Stokes system of equations, Comm. Math. Phys.281 (2008) 573-596. · Zbl 1155.35415
[25] Moussa, A., Some variants of the classical Aubin-Lions Lemma, J. Evol. Equ.16 (2016) 65-93. · Zbl 1376.46015
[26] Williams, F. A., Combustion Theory, 2nd edn. (Benjamin Cummings, 1985).
[27] Yu, C., Global weak solutions to the incompressible Navier-Stokes-Vlasov equations, J. Math. Pures Appl. (9), 100 (2013) 275-293. · Zbl 1284.35119
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