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Global weak solutions to a Vlasov‐Fokker‐Planck/compressible non‐Newtonian fluid system of equations
Author(s) -
Zhu Huan,
Fang Li,
Muhammad Jan,
Guo Zhenhua
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900091
Subject(s) - bounded function , fokker–planck equation , domain (mathematical analysis) , weak solution , compressibility , physics , classical mechanics , mathematics , compact space , vector field , boundary value problem , compressible flow , bbgky hierarchy , mathematical analysis , partial differential equation , mechanics , quantum mechanics , distribution function
This article is devoted to a coupled microscopic/macroscopic model describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov‐Fokker‐Planck equation to describe the microscopic motion of the particles coupled to the equations for a compressible non‐Newtonian fluid. An initial‐boundary value problem is studied in a bounded domain with the divergence of the velocity field keeping bounded. The existence of global weak solution is established through an approximation scheme, a fixed point argument, the lower semi‐continuity of monotone operators, energy estimates and the principle of compensated compactness.