Analysis for symmetric and non-decaying viscous incompressible flows

2016 Fiscal Year Final Research Report

• Project/Area Number: 15H06312
• Research Category: Grant-in-Aid for Research Activity Start-up
• Allocation Type: Single-year Grants
• Research Field: Mathematical analysis
• Research Institution: Kyoto University
• Principal Investigator: Abe Ken 京都大学, スーパーグローバルコース数学系ユニット, 特定助教 (80748327)
• Project Period (FY): 2015-08-28 – 2017-03-31
• Keywords: ナヴィエ・ストークス方程式 / 有界関数空間 / ストークス半群 / 解析半群 / 軸対称解 / 外部問題

Outline of Final Research Achievements

I have studied regularity and asymptotic behavior of solutions for the Navier-Stokes equations, which describes the motion of viscous incompressible flows such as the atmosphere and the water. In this research project, I have worked on the two problems.
The first problem is an axisymmetric solution. I have constructed global unique axisymmetric solutions in an exterior domain subject to the slip boundary condition for decaying and sufficiently smooth initial data.
The second is a non-decaying solution. I have constructed local-in-time unique solutions in an exterior domain in a space of bounded functions. For the two-dimensional case, I have proved that global unique solutions exist for bounded initial data with a finite Dirichlet integral.

Free Research Field

偏微分方程式論