Weak solution to a one‐dimensional full compressible non‐Newtonian fluid. (23rd March 2018)

• Record Type: Journal Article
• Authors: Fang, Li; Kong, Xiaojing; Liu, Jinjing
• Is Part Of: Mathematical methods in the applied sciences. Volume 41:Number 9(2018)
• Page Start: 3441
• Page End: 3462
• Publication Date: 2018-03-23
• Subjects: compressible non‐Newtonian fluid -- numerical simulations -- weak solutions; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4837
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : 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.