Mathematical analysis of low-dimensional dynamical system of plasma turbulence

2023 Fiscal Year Final Research Report

• Project/Area Number: 20K03745
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Review Section: Basic Section 12040:Applied mathematics and statistics-related
• Research Institution: Gifu University
• Principal Investigator: Kondo Shintaro 岐阜大学, 工学部, 准教授 (60726371)
• Project Period (FY): 2020-04-01 – 2024-03-31
• Keywords: 偏微分方程式 / 常微分方程式 / プラズマ

Outline of Final Research Achievements

For the Sugama-Horton model, a three-variable ordinary differential equation describing plasma, we considered the case in which the dissipation coefficient of the equation for turbulent energy k is constant and the external force q is constant, and proved the existence of a global-in-time solution, and positivity of solution. We also showed that when q is small, the steady-state solution for L-mode (i.e., zonal flow energy f=0) is globally asymptotically stable.
For the simplified MHD equations studied in papers by M. Ottaviani and M. Muraglia, we proved the existence theorem under periodic boundary conditions. For the MHD equations with an external shear flow, we proved the existence theorem under shearing-periodic boundary conditions.

Free Research Field

非線形偏微分方程式

Academic Significance and Societal Importance of the Research Achievements

核融合プラズマの主要な研究課題のひとつに、シアー流れの効果の研究がある。例えば、Sugama-Hortonモデルは、プラズマが乱流状態にあるときから、帯状の流れ（帯状流・シアー流れ）が支配的なときへの相転移現象を説明するモデルである。また、Hawley他は１９９５年の論文においてshearing-periodic境界条件を用いて天体の降着円盤の数値シミュレーションを行った。本研究で得られた成果は、数値シミュレーション及び数学解析の立場から、Sugama-Hortonモデルやshearing-periodic境界条件の応用に関する研究成果を得たという意義がある。