Mathematical analysis of an incompressible viscous fluid in an infinite layer by methods of real analysis

Research Project

Project/Area Number	20740083
Research Category	Grant-in-Aid for Young Scientists (B)
Allocation Type	Single-year Grants
Research Field	Basic analysis
Research Institution	Kisarazu National College of Technology
Principal Investigator	ABE Takayuki 木更津工業高等専門学校, 基礎学系, 准教授 (70396274)
Project Period (FY)	2008 – 2011
Project Status	Completed (Fiscal Year 2011)
Budget Amount *help	¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000) Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000) Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000) Fiscal Year 2009: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000) Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords	Navier-Stokes方程式 / Stokes方程式 / レゾルベント評価 / 解析的半群 / 自由境界問題 / Besov空間 / 斉次Besov空間 / Maximal regularity / Maximal Regularity / 境界値問題
Research Abstract	We analyze a resolvent problem of the Stokes equation in an infinite layer and prove that the Stokes operator generates an analytic semigroup on Holder and Besov spaces. As an application, we prove a stability of some special solutions in Besov spaces. Moreover, we prove maximal regularity for the Stokes equation by operator-valued Fourier multiplier theorem, and we prove unique existence of a local in time solution to free boundary problems of the Navier-Stokes equation.

Report

(6 results)