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Weak solution to a one‐dimensional full compressible non‐Newtonian fluid
Author(s) -
Fang Li,
Kong Xiaojing,
Liu Jinjing
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4837
Subject(s) - mathematics , convexity , compressibility , convergence (economics) , weak solution , mathematical analysis , newtonian fluid , compact space , non newtonian fluid , projection method , projection (relational algebra) , finite element method , compressible flow , scheme (mathematics) , mathematical optimization , classical mechanics , dykstra's projection algorithm , algorithm , mechanics , physics , financial economics , economics , thermodynamics , economic growth
This paper is devoted to the existence of global‐in‐time weak solutions to a one‐dimensional full compressible non‐Newtonian fluid. A semi‐discrete finite element scheme is taken to generate approximate solutions, based on an exact projection technique. To enforce convergence of the approximate solutions, the uniform estimate is obtained using an iteration method and energy method, with the help of the weak compactness and convexity. Numerical simulations showing the existence of solutions are presented.