O. Anoshchenko, E. Khruslov, H. Stephan, “Global weak solutions to the Navier–Stokes–Vlasov–Poisson system”, Zh. Mat. Fiz. Anal. Geom., 2010, Volume 6, Number 2,Pages <nobr>143

This article is cited in 6 papers

Global weak solutions to the Navier–Stokes–Vlasov–Poisson system

O. Anoshchenko^a, E. Khruslov^b, H. Stephan^c

^a Department of Mechanics and Mathematics, V. N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61077, Ukraine
^b Mathematical Division, B. Verkin Institute for Low Temperature Physics and Engineering, 47 Lenin Ave., Kharkiv, 61103, Ukraine
^c Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, Berlin, D-10117, Germany

Abstract: We consider the Navier–Stokes–Vlasov–Poisson system describing the flow of a viscous incompressible fluid containing small solid charged particles. The existence result for weak global solutions of the corresponding boundary value problem is obtained.

Key words and phrases: Navier–Stokes equation, Vlasov–Poisson equation, suspensions, global weak solution, modified Galerkin method, compactness of approximations.

MSC: 76D05, 35J05, 76T20

Received: 11.11.2009