Boudin, Laurent; Grandmont, Céline; Moussa, Ayman Global existence of solutions to the incompressible Navier-Stokes-Vlasov equations in a time-dependent domain. (English) Zbl 1371.35214 J. Differ. Equations 262, No. 3, 1317-1340 (2017). This article deals with the incompressible Navier-Stokes-Vlasov system in a three-dimensional time-dependent domain. The authors present the global existence of solutions for this problem, when absorption boundary conditions for the kinetic part are considered. These boundary conditions lead to the necessity of working with weak solutions. Another difficulty of the considered problem is represented by the fact that the approximation procedure of the system has to take into account the time-dependence of the domain; this is analyzed with a penalization method.After the presentation of the problem and the definition of a weak solution to this problem, the main result of the article is given. This result is obtained by means of an approximated system, solved with a fix-point method. The existence of solutions for the approximated system allows to obtain finally a weak solution for the initial problem. Reviewer: Ruxandra Stavre (Bucureşti) Cited in 19 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 35Q83 Vlasov equations 35D30 Weak solutions to PDEs 35A01 Existence problems for PDEs: global existence, local existence, non-existence Keywords:Navier-Stokes-Vlasov system; absorption boundary conditions; weak solution PDFBibTeX XMLCite \textit{L. Boudin} et al., J. Differ. Equations 262, No. 3, 1317--1340 (2017; Zbl 1371.35214) Full Text: DOI References: [1] Anoshchenko, O.; Boutet de Monvel-Berthier, A., The existence of the global generalized solution of the system of equations describing suspension motion, Math. Methods Appl. 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