Analysis of mathematical structure of pattern dynamics for compressible fluid

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K22308
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Multi-year Fund
• Review Section: 0201:Algebra, geometry, analysis, applied mathematics,and related fields
• Research Institution: Ehime University (2021-2023); Okayama University (2020)
• Principal Investigator: Teramoto Yuka 愛媛大学, 理工学研究科(理学系), 助教 (60883262)
• Project Period (FY): 2020-09-11 – 2024-03-31
• Keywords: 圧縮性Navier-Stokes方程式 / 液晶 / 漸近挙動

Outline of Final Research Achievements

I studied about liquid crystals which have the property of being anisotropic. Ericksen-Leslie system couples the Navier-Stokes equations governing the fluid velocity with direction equation governing the motion of orientation of rod-like particles. I proved the existence of global strong solutions, its decay rates and the asymptotic behavior for non-isothermal simplified Ericksen-Leslie system in infinite layer. It turns out that the low-frequency part of the solution decays like a 2-dimensional heat kernel. We can also see that the low-frequency part appears in the asymptotic reading part of the solution which is affected by nonlinear terms as time goes to infinity.

Free Research Field

数学

Academic Significance and Societal Importance of the Research Achievements

Ericksen-Leslie systemは液晶の流れを記述する方程式であり，流体の運動や，細長い棒状分子の向きや曲げ伸ばしの影響も考慮されている．そのため豊富な非線形相互作用を観察することができ，学術的価値がある．液晶は温度によってその様相を変化させるが，非等温下での解析を行った結果は少ない．温度を変数として加えた方程式の解析は物理学，工学にも寄与するものと考えられる．