On the R-Sectoriality and the Initial Boundary Value Problem for the Viscous Compressible Fluid Flow

被引：53

作者：

Enomoto, Yuko ^{[1
]}

Shibata, Yoshihiro ^{[2
,3
]}

机构：

[1] Shibaura Inst Technol, Dept Math Sci, Minuma Ku, Saitama 3378570, Japan

[2] Waseda Univ, Dept Math, Shinjuku Ku, Tokyo 1698555, Japan

[3] Waseda Univ, Res Inst Sci & Engn, Shinjuku Ku, Tokyo 1698555, Japan

来源：

FUNKCIALAJ EKVACIOJ-SERIO INTERNACIA | 2013年 / 56卷 / 03期

关键词：

Compressible viscous fluid; Navier-Stokes equations; Stokes equations; R-sectoriality; General domain; Analytic semigroup; Maximal L-p-L-q regularity; Exponential stability; Local in time unique existence theorem; Global in time unique existence theorem; NAVIER-STOKES EQUATIONS; LARGE-TIME BEHAVIOR; ASYMPTOTIC-BEHAVIOR; MAXIMAL REGULARITY; RESOLVENT; EXISTENCE; OPERATOR; SEMIGROUP; SYSTEM;

D O I：

10.1619/fesi.56.441

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the R-sectoriality of the resolvent problem for the boundary value problem of the Stokes operator for the compressible viscous fluids in a general domain, which implies the generation of analytic semigroup and the maximal L-p-L-q regularity for the initial boundary value problem of the Stokes operator. Combining our linear theory with fixed point arguments in the Lagrangian coordinates, we have a local in time unique existence theorem in a general domain and a global in time unique existence theorem for some initial data close to a constant state in a bounded domain for the initial boundary value problem of the Navier-Stokes equations describing the motion of compressible viscous fluids. All the results obtained in this paper were announced in Enomoto-Shibata [12].

引用

页码：441 / 505

页数：65