Mathematical analysis of the non-Newtonian fluids flow

2014 Fiscal Year Final Research Report

• Project/Area Number: 23654055
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Basic analysis
• Research Institution: Keio University
• Principal Investigator: TANI Atusi 慶應義塾大学, 理工学部, 名誉教授 (90118969)
• Co-Investigator(Kenkyū-buntansha): IGUCHI Tatsuo 慶應義塾大学, 理工学部, 教授 (20294879) ; TAKAYAMA Masahiro 慶應義塾大学, 理工学部, 助教 (90338252) ; NDERA Takashi 慶應義塾大学, 理工学部, 教授 (50156212)
• Co-Investigator(Renkei-kenkyūsha): ITOH Shigeharu 弘前大学, 教育学部, 教授 (40193487) ; TANAKA Naoto 福岡大学, 理学部, 教授 (00247222) ; ITOU Hiromichi 東京理科大学, 理学部第二部, 専任講師 (30400790) ; UMEHARA Morimichi 宮崎大学, 工学部, 准教授 (40532164)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 非ニュートン流体流 / Maxwell fluid / Navier’s slip condition / Hele-Shaw flow / elastic body / primitive equation / water wave / Hasegawa-Wakatani 方程式

Outline of Final Research Achievements

Well-posedness of nonlinear problems for various natural phenomena, especially of those described as non-Newtonian fluids flow was established mathematically. Some of research results are as follows.
(1) For a non-Newtonian fluid flow, especially for the 2-dimensional flow of incompressible viscoelastic Maxwell media with a Jaumann corotational derivative in the rheological constitutive law we proved that the discontinuity can develop even from smooth initial data, and the stability of shocks in it without retardation. (2) An equilibrium problem for 2-dimensional homogeneous isotropic linearized elasticity with a rigid line inclusion was studied in both not delaminated and laminated cases, and investigated an asymptotic behavior of a solution near a tip of a rigid line inclusion. (3) The fingering pattern of radially growing interface in a Hele-Shaw cell was shown in the framework of weakly nonlinear analysis under the wetting layer effect of the displacing fluid taken into account.

Free Research Field

非線形解析, 数理物理